Question 1

The sum of the squares of two consecutive, positive even integers is 164. Find the integers.

Accepted Answer

A)  6, 8 
B)  10, 12 
C)  4, 6 
D)  8, 10 
A)  6, 8 
B)  10, 12 
C)  4, 6 
D)  8, 10

Question 2

Simplify the expression. Write your answer with positive exponents only. $\left( x ^ { 9 } \right) ^ { 5 }$

Accepted Answer

A)  $x ^ { 59,049 }$ 
B)  $x ^ { 4 }$ 
C)  $x ^ { 45 }$ 
D)  $x ^ { 14 }$ 
A)  $x ^ { 59,049 }$ 
B)  $x ^ { 4 }$ 
C)  $x ^ { 45 }$ 
D)  $x ^ { 14 }$

Question 3

Factor out the greatest common factor. Then determine if the polynomial is a perfect square trinomial. If it is, factor it. $16 m ^ { 2 } + 72 m + 81$

Accepted Answer

A)  $( 4 m - 9 ) ^ { 2 }$ 
B)  $( 4 m + 9 ) ^ { 2 }$ 
C)  $16 ( m + 9 ) ^ { 2 }$ 
D)  Not a perfect square trinomial 
A)  $( 4 m - 9 ) ^ { 2 }$ 
B)  $( 4 m + 9 ) ^ { 2 }$ 
C)  $16 ( m + 9 ) ^ { 2 }$ 
D)  Not a perfect square trinomial

Question 4

Add or subtract as indicated. Write the answer in descending order. $$\left( 3 n ^ { 4 } + 1 \right) + \left( - 8 n ^ { 4 } + 3 \right) - \left( - 8 n ^ { 4 } + 2 \right)$$

Accepted Answer

A)  $3 n ^ { 4 } + 6$ 
B)  $- 13 n ^ { 4 } + 6$ 
C)  $3 n ^ { 4 } + 2$ 
D)  $19 n ^ { 4 } - 4$ 
A)  $3 n ^ { 4 } + 6$ 
B)  $- 13 n ^ { 4 } + 6$ 
C)  $3 n ^ { 4 } + 2$ 
D)  $19 n ^ { 4 } - 4$

Question 5

Factor the trinomial completely by using any method. Remember to look for a common factor first. $6 r ^ { 2 } - 35 r - 49$

Accepted Answer

A)  Prime 
B)  $r ( 6 r - 35 ) - 49$ 
C)  $( 6 r + 7 ) ( r - 7 )$ 
D)  $( 6 r + 7 ) ( r + 7 )$ 
A)  Prime 
B)  $r ( 6 r - 35 ) - 49$ 
C)  $( 6 r + 7 ) ( r - 7 )$ 
D)  $( 6 r + 7 ) ( r + 7 )$

Question 6

The square of a number is equal to 6 more than the number. Find all such numbers.

Accepted Answer

A)  -3 
B)  3; -2 
C)  -3; 4 
D)  -4; -3 
A)  -3 
B)  3; -2 
C)  -3; 4 
D)  -4; -3

Question 7

Determine which of the following equations are written in the correct form to apply the zero product rule directly. i. $( x - 9 ) ( x + 7 ) = 0$
ii. $x ( x - 9 ) = 7$
iii. $x ( x + 7 ) = 0$
iv. $x ^ { 2 } - 2 x - 63 = 0$

Accepted Answer

A)  i, iii 
B)  i, ii, iii 
C)  i 
D)  i, iii, iv 
A)  i, iii 
B)  i, ii, iii 
C)  i 
D)  i, iii, iv

Question 8

Simplify the expression. Write your answer with positive exponents only. $\left( \frac { t } { 2 } \right) ^ { 4 }$

Accepted Answer

A)  $t ^ { 4 } - 16$ 
B)  $\frac { t ^ { 4 } } { 16 }$ 
C)  $\frac { t } { 16 }$ 
D)  $\frac { t ^ { 4 } } { 2 }$ 
A)  $t ^ { 4 } - 16$ 
B)  $\frac { t ^ { 4 } } { 16 }$ 
C)  $\frac { t } { 16 }$ 
D)  $\frac { t ^ { 4 } } { 2 }$

Question 9

Factor the trinomial completely by using any method. Remember to look for a common factor first. $$2 m ^ { 2 } + 4 m - 70$$

Accepted Answer

A)  $2 ( m - 5 ) ( m + 7 )$ 
B)  $2 m ( m + 2 ) - 70$ 
C)  $2 ( m + 5 ) ( m - 7 )$ 
D)  Prime 
A)  $2 ( m - 5 ) ( m + 7 )$ 
B)  $2 m ( m + 2 ) - 70$ 
C)  $2 ( m + 5 ) ( m - 7 )$ 
D)  Prime

Question 10

Factor completely using the difference of squares along with factoring by grouping. $2 t - 2 u + t ^ { 2 } - u ^ { 2 }$

Accepted Answer

A)  $( t - u ) ( 2 + t + u )$ 
B)  $2 ( t - u ) ( t + u )$ 
C)  $2 ( t - u ) + t ^ { 2 } + u ^ { 2 }$ 
D)  Prime 
A)  $( t - u ) ( 2 + t + u )$ 
B)  $2 ( t - u ) ( t + u )$ 
C)  $2 ( t - u ) + t ^ { 2 } + u ^ { 2 }$ 
D)  Prime

Question 11

Solve the equation. $$z ^ { 2 } + ( z + 1 ) ^ { 2 } = 85$$

Accepted Answer

A)  $z = 7 ; z = - 6$ 
B)  $z = - 7 ; z = 6$ 
C)  $z = 7 ; z = 6$ 
D)  $z = 0 ; z = - 1$ 
A)  $z = 7 ; z = - 6$ 
B)  $z = - 7 ; z = 6$ 
C)  $z = 7 ; z = 6$ 
D)  $z = 0 ; z = - 1$

Question 12

Factor the trinomial completely by using any method. Remember to look for a common factor first. $12 m n ^ { 2 } - 87 m n + 90 m$

Accepted Answer

A)  $( 4 n - 5 ) ( 3 m n - 18 m )$ 
B)  $3 m ( 4 n + 5 ) ( n + 6 )$ 
C)  $3 m ( 4 n - 5 ) ( n - 6 )$ 
D)  Prime 
A)  $( 4 n - 5 ) ( 3 m n - 18 m )$ 
B)  $3 m ( 4 n + 5 ) ( n + 6 )$ 
C)  $3 m ( 4 n - 5 ) ( n - 6 )$ 
D)  Prime

Question 13

Factor out the indicated quantity. $- 36 y ^ { 5 } z + 36 y ^ { 4 } z + 20 y ^ { 3 } z$ : Factor out the quantity $- 4 y ^ { 3 } z$

Accepted Answer

A)  $- 4 y ^ { 3 } z \left( - 9 y ^ { 2 } + 9 y + 5 \right)$ 
B)  $- 4 y ^ { 3 } z \left( 9 y ^ { 3 } - 9 y ^ { 2 } - 5 \right)$ 
C)  $- 4 y ^ { 3 } z \left( 9 y ^ { 2 } - 9 y - 5 \right)$ 
D)  $- 4 y ^ { 3 } z \left( - 9 y ^ { 2 } - 9 y - 5 \right)$ 
A)  $- 4 y ^ { 3 } z \left( - 9 y ^ { 2 } + 9 y + 5 \right)$ 
B)  $- 4 y ^ { 3 } z \left( 9 y ^ { 3 } - 9 y ^ { 2 } - 5 \right)$ 
C)  $- 4 y ^ { 3 } z \left( 9 y ^ { 2 } - 9 y - 5 \right)$ 
D)  $- 4 y ^ { 3 } z \left( - 9 y ^ { 2 } - 9 y - 5 \right)$

Question 14

Translate from English form to algebraic form. The cube of the sum of p and q

Accepted Answer

A)  $( p + q ) ^ { 3 }$ 
B)  $\left( p ^ { 2 } + q ^ { 2 } \right) ^ { 3 }$ 
C)  $p ^ { 3 } + q ^ { 3 }$ 
D)  $( p + q ) ^ { 2 }$ 
A)  $( p + q ) ^ { 3 }$ 
B)  $\left( p ^ { 2 } + q ^ { 2 } \right) ^ { 3 }$ 
C)  $p ^ { 3 } + q ^ { 3 }$ 
D)  $( p + q ) ^ { 2 }$

Question 15

Factor out the GCF. $$6 y ( y - 8 ) ^ { 2 } + 3 ( y - 8 ) ^ { 2 }$$

Accepted Answer

A)  $3 ( y - 8 ) ^ { 2 } ( 2 y + 1 )$ 
B)  $3 \left( 2 y ( y - 8 ) ^ { 2 } + 1 ( y - 8 ) ^ { 2 } \right)$ 
C)  $( y - 8 ) ^ { 2 } ( 6 y + 3 )$ 
D)  $6 \left( ( y - 8 ) ^ { 2 } + 1 ( y - 8 ) ^ { 2 } \right)$ 
A)  $3 ( y - 8 ) ^ { 2 } ( 2 y + 1 )$ 
B)  $3 \left( 2 y ( y - 8 ) ^ { 2 } + 1 ( y - 8 ) ^ { 2 } \right)$ 
C)  $( y - 8 ) ^ { 2 } ( 6 y + 3 )$ 
D)  $6 \left( ( y - 8 ) ^ { 2 } + 1 ( y - 8 ) ^ { 2 } \right)$

Question 16

The earth is abo $9.3 \times 10 ^ { 7 }$ miles from the sun, and about 2.39 × $2.39 \times 10 ^ { 5 }$ from the moon. What percentage of the larger distance is the smaller (to the nearest hundredth of a percent)?

Accepted Answer

The answer of The earth is abo \(9.3 \times 10...

Question 17

Write the polynomial in descending order. Then identify the leading coefficient and the degree. $$- 2 x + 8 + 2 x ^ { 4 }$$

Accepted Answer

A)  $8 + 2 x ^ { 4 } - 2 x$; leading coefficient: 8 ; degree: 4 
B)  $2 x ^ { 4 } - 2 x + 8$; leading coefficient: 2 ; degree: 4 
C)  $2 x ^ { 4 } - 2 x + 8$; leading coefficient: 2 ; degree: 3 
D)  $8 + 2 x ^ { 4 } - 2 x$; leading coefficient: 8 ; degree: 3 
A)  $8 + 2 x ^ { 4 } - 2 x$; leading coefficient: 8 ; degree: 4 
B)  $2 x ^ { 4 } - 2 x + 8$; leading coefficient: 2 ; degree: 4 
C)  $2 x ^ { 4 } - 2 x + 8$; leading coefficient: 2 ; degree: 3 
D)  $8 + 2 x ^ { 4 } - 2 x$; leading coefficient: 8 ; degree: 3

Question 18

Factor the expression that defines the function. $k ( w ) = w ^ { 3 } + 7 w ^ { 2 } + 4 w + 28$

Accepted Answer

A)  $k ( w ) = ( w + 7 ) \left( w ^ { 2 } + 4 \right)$ 
B)  $k ( w ) = w ^ { 2 } ( w + 7 ) + 2 ( 2 w + 14 )$ 
C)  $k ( w ) = ( w + 7 ) ( w + 2 ) ( w - 2 )$ 
D)  $k ( w ) = w ^ { 3 } + 7 w ^ { 2 } + 4 w + 28$ (Expression is prime) 
A)  $k ( w ) = ( w + 7 ) \left( w ^ { 2 } + 4 \right)$ 
B)  $k ( w ) = w ^ { 2 } ( w + 7 ) + 2 ( 2 w + 14 )$ 
C)  $k ( w ) = ( w + 7 ) ( w + 2 ) ( w - 2 )$ 
D)  $k ( w ) = w ^ { 3 } + 7 w ^ { 2 } + 4 w + 28$ (Expression is prime)

Question 19

Translate from English form to algebraic form. The cube of v, minus the square of w

Accepted Answer

A)  $v ^ { 3 } - w ^ { 2 }$ 
B)  $\left( ( v - w ) ^ { 3 } \right) ^ { 2 }$ 
C)  $\left( v ^ { 3 } - w \right) ^ { 2 }$ 
D)  $\left( v - w ^ { 2 } \right) ^ { 3 }$ 
A)  $v ^ { 3 } - w ^ { 2 }$ 
B)  $\left( ( v - w ) ^ { 3 } \right) ^ { 2 }$ 
C)  $\left( v ^ { 3 } - w \right) ^ { 2 }$ 
D)  $\left( v - w ^ { 2 } \right) ^ { 3 }$

Question 20

Simplify the expression. Write your answer with positive exponents only. $$\frac { - 54 a ^ { 9 } b ^ { 6 } } { 12 a ^ { 2 } b ^ { 9 } }$$

Accepted Answer

A)  $- \frac { 9 a ^ { 11 } b ^ { 3 } } { 2 }$ 
B)  $\frac { 9 a ^ { 7 } } { 2 b ^ { 3 } }$ 
C)  $- \frac { 9 a ^ { 7 } } { 2 b ^ { 3 } }$ 
D)  $- \frac { 9 b ^ { 3 } } { a ^ { 7 } }$ 
A)  $- \frac { 9 a ^ { 11 } b ^ { 3 } } { 2 }$ 
B)  $\frac { 9 a ^ { 7 } } { 2 b ^ { 3 } }$ 
C)  $- \frac { 9 a ^ { 7 } } { 2 b ^ { 3 } }$ 
D)  $- \frac { 9 b ^ { 3 } } { a ^ { 7 } }$

The sum of the squares of two consecutive, positive even integers is 164. Find the integers.

Simplify the expression. Write your answer with positive exponents only. $\left( x ^ { 9 } \right) ^ { 5 }$

Factor out the greatest common factor. Then determine if the polynomial is a perfect square trinomial. If it is, factor it. $16 m ^ { 2 } + 72 m + 81$

Add or subtract as indicated. Write the answer in descending order. $\left( 3 n ^ { 4 } + 1 \right) + \left( - 8 n ^ { 4 } + 3 \right) - \left( - 8 n ^ { 4 } + 2 \right)$

Factor the trinomial completely by using any method. Remember to look for a common factor first. $6 r ^ { 2 } - 35 r - 49$

The square of a number is equal to 6 more than the number. Find all such numbers.

Determine which of the following equations are written in the correct form to apply the zero product rule directly. i. $( x - 9 ) ( x + 7 ) = 0$ ii. $x ( x - 9 ) = 7$ iii. $x ( x + 7 ) = 0$ iv. $x ^ { 2 } - 2 x - 63 = 0$

Simplify the expression. Write your answer with positive exponents only. $\left( \frac { t } { 2 } \right) ^ { 4 }$

Factor the trinomial completely by using any method. Remember to look for a common factor first. $2 m ^ { 2 } + 4 m - 70$

Factor completely using the difference of squares along with factoring by grouping. $2 t - 2 u + t ^ { 2 } - u ^ { 2 }$

Solve the equation. $z ^ { 2 } + ( z + 1 ) ^ { 2 } = 85$

Factor the trinomial completely by using any method. Remember to look for a common factor first. $12 m n ^ { 2 } - 87 m n + 90 m$

Factor out the indicated quantity. $- 36 y ^ { 5 } z + 36 y ^ { 4 } z + 20 y ^ { 3 } z$ : Factor out the quantity $- 4 y ^ { 3 } z$

Translate from English form to algebraic form. The cube of the sum of p and q

Factor out the GCF. $6 y ( y - 8 ) ^ { 2 } + 3 ( y - 8 ) ^ { 2 }$

The earth is abo $9.3 \times 10 ^ { 7 }$ miles from the sun, and about 2.39 × $2.39 \times 10 ^ { 5 }$ from the moon. What percentage of the larger distance is the smaller (to the nearest hundredth of a percent)?

Write the polynomial in descending order. Then identify the leading coefficient and the degree. $- 2 x + 8 + 2 x ^ { 4 }$

Factor the expression that defines the function. $k ( w ) = w ^ { 3 } + 7 w ^ { 2 } + 4 w + 28$

Translate from English form to algebraic form. The cube of v, minus the square of w

Simplify the expression. Write your answer with positive exponents only. $\frac { - 54 a ^ { 9 } b ^ { 6 } } { 12 a ^ { 2 } b ^ { 9 } }$

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Exam 4: Polynomials

The sum of the squares of two consecutive, positive even integers is 164. Find the integers.

Simplify the expression. Write your answer with positive exponents only. (x9)5\left( x ^ { 9 } \right) ^ { 5 }(x9)5

Factor out the greatest common factor. Then determine if the polynomial is a perfect square trinomial. If it is, factor it. 16m2+72m+8116 m ^ { 2 } + 72 m + 8116m2+72m+81

Add or subtract as indicated. Write the answer in descending order. (3n4+1)+(−8n4+3)−(−8n4+2)\left( 3 n ^ { 4 } + 1 \right) + \left( - 8 n ^ { 4 } + 3 \right) - \left( - 8 n ^ { 4 } + 2 \right)(3n4+1)+(−8n4+3)−(−8n4+2)

Factor the trinomial completely by using any method. Remember to look for a common factor first. 6r2−35r−496 r ^ { 2 } - 35 r - 496r2−35r−49

The square of a number is equal to 6 more than the number. Find all such numbers.

Simplify the expression. Write your answer with positive exponents only. (t2)4\left( \frac { t } { 2 } \right) ^ { 4 }(2t​)4

Factor the trinomial completely by using any method. Remember to look for a common factor first. 2m2+4m−702 m ^ { 2 } + 4 m - 702m2+4m−70

Factor completely using the difference of squares along with factoring by grouping. 2t−2u+t2−u22 t - 2 u + t ^ { 2 } - u ^ { 2 }2t−2u+t2−u2

Solve the equation. z2+(z+1)2=85z ^ { 2 } + ( z + 1 ) ^ { 2 } = 85z2+(z+1)2=85

Factor the trinomial completely by using any method. Remember to look for a common factor first. 12mn2−87mn+90m12 m n ^ { 2 } - 87 m n + 90 m12mn2−87mn+90m

Factor out the indicated quantity. −36y5z+36y4z+20y3z- 36 y ^ { 5 } z + 36 y ^ { 4 } z + 20 y ^ { 3 } z−36y5z+36y4z+20y3z : Factor out the quantity −4y3z- 4 y ^ { 3 } z−4y3z

Translate from English form to algebraic form. The cube of the sum of p and q

Factor out the GCF. 6y(y−8)2+3(y−8)26 y ( y - 8 ) ^ { 2 } + 3 ( y - 8 ) ^ { 2 }6y(y−8)2+3(y−8)2

The earth is abo 9.3×1079.3 \times 10 ^ { 7 }9.3×107 miles from the sun, and about 2.39 × 2.39×1052.39 \times 10 ^ { 5 }2.39×105 from the moon. What percentage of the larger distance is the smaller (to the nearest hundredth of a percent)?

Write the polynomial in descending order. Then identify the leading coefficient and the degree. −2x+8+2x4- 2 x + 8 + 2 x ^ { 4 }−2x+8+2x4

Factor the expression that defines the function. k(w)=w3+7w2+4w+28k ( w ) = w ^ { 3 } + 7 w ^ { 2 } + 4 w + 28k(w)=w3+7w2+4w+28

Translate from English form to algebraic form. The cube of v, minus the square of w

Simplify the expression. Write your answer with positive exponents only. −54a9b612a2b9\frac { - 54 a ^ { 9 } b ^ { 6 } } { 12 a ^ { 2 } b ^ { 9 } }12a2b9−54a9b6​

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Simplify the expression. Write your answer with positive exponents only. $\left( x ^ { 9 } \right) ^ { 5 }$

Factor out the greatest common factor. Then determine if the polynomial is a perfect square trinomial. If it is, factor it. $16 m ^ { 2 } + 72 m + 81$

Add or subtract as indicated. Write the answer in descending order. $\left( 3 n ^ { 4 } + 1 \right) + \left( - 8 n ^ { 4 } + 3 \right) - \left( - 8 n ^ { 4 } + 2 \right)$

Factor the trinomial completely by using any method. Remember to look for a common factor first. $6 r ^ { 2 } - 35 r - 49$

Simplify the expression. Write your answer with positive exponents only. $\left( \frac { t } { 2 } \right) ^ { 4 }$

Factor the trinomial completely by using any method. Remember to look for a common factor first. $2 m ^ { 2 } + 4 m - 70$

Factor completely using the difference of squares along with factoring by grouping. $2 t - 2 u + t ^ { 2 } - u ^ { 2 }$

Solve the equation. $z ^ { 2 } + ( z + 1 ) ^ { 2 } = 85$

Factor the trinomial completely by using any method. Remember to look for a common factor first. $12 m n ^ { 2 } - 87 m n + 90 m$

Factor out the indicated quantity. $- 36 y ^ { 5 } z + 36 y ^ { 4 } z + 20 y ^ { 3 } z$ : Factor out the quantity $- 4 y ^ { 3 } z$

Factor out the GCF. $6 y ( y - 8 ) ^ { 2 } + 3 ( y - 8 ) ^ { 2 }$

The earth is abo $9.3 \times 10 ^ { 7 }$ miles from the sun, and about 2.39 × $2.39 \times 10 ^ { 5 }$ from the moon. What percentage of the larger distance is the smaller (to the nearest hundredth of a percent)?

Write the polynomial in descending order. Then identify the leading coefficient and the degree. $- 2 x + 8 + 2 x ^ { 4 }$

Factor the expression that defines the function. $k ( w ) = w ^ { 3 } + 7 w ^ { 2 } + 4 w + 28$

Simplify the expression. Write your answer with positive exponents only. $\frac { - 54 a ^ { 9 } b ^ { 6 } } { 12 a ^ { 2 } b ^ { 9 } }$