Fill in the blank with one of the words or phrases listed below. Not all choices will be used and some choices may be used more than once. \[\begin{array} { l l l l } \text { factoring } & \text { quadratic equation } & \text { perfect square trinomial } & 0 \\ \text { greatest common factor } & \text { hypotenuse } & \text { sum of two cubes } & 1 \\ \text { difference of two cubes } & \text { difference of two squares } & \text { triangle } & \text { leg } \end{array}\] -The expression $a ^ { 2 } - b ^ { 2 }$ is called a_______

A) difference of two squares B) sum of two cubes C) perfect square trinomial D) difference of two cubes A) difference of two squares B) sum of two cubes C) perfect square trinomial D) difference of two cubes

Fill in the blank with one of the words or phrases listed below. Not all choices will be used and some choices may be used more than once. \[\begin{array} { l l l l } \text { factoring } & \text { quadratic equation } & \text { perfect square trinomial } & 0 \\ \text { greatest common factor } & \text { hypotenuse } & \text { sum of two cubes } & 1 \\ \text { difference of two cubes } & \text { difference of two squares } & \text { triangle } & \text { leg } \end{array}\] -In a right triangle, the side opposite the right angle is called the ________

A) leg B) quadratic equation C) hypotenuse D) triangle A) leg B) quadratic equation C) hypotenuse D) triangle

Exam 6: Factoring Polynomials

Solve. -Within a group of $\mathrm { n }$ people, the number of possible handshakes, $N$ , is given by $\mathrm { N } = \frac { 1 } { 2 } \left( \mathrm { n } ^ { 2 } - \mathrm { n } \right)$ . How many handshakes are possible at a meeting if 16 people are present?

(Multiple Choice)

4.9/5

(95)

Question 241

Factor completely. - $12 x ^ { 2 } + 17 x + 6$

(Multiple Choice)

4.8/5

(88)

Question 242

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $2 x ^ { 2 } - 19 x + 45$

(Multiple Choice)

5.0/5

(83)

Question 243

Factor out the GCF from the polynomial. - $28 m ^ { 8 } - 8 m ^ { 6 } + 28 m ^ { 4 }$

(Multiple Choice)

4.8/5

(79)

Question 244

Solve. -Two vehicles leave the same corner at the same time and travel at a right angle to each other. One vehicle travels 2 kilometers an hour faster than the other. If after one hour the vehicles are 10 kilometers apart, find the rate of each vehicle.

(Multiple Choice)

4.9/5

(69)

Question 245

Factor completely. - $9 x ^ { 2 } + x - 140$

(Multiple Choice)

4.8/5

(81)

Question 246

Factor the sum or difference of two cubes. - $512 - t ^ { 3 }$

(Multiple Choice)

4.9/5

(73)

Question 247

Solve the equation. - $x ^ { 2 } + 5 x - 36 = 0$

(Multiple Choice)

4.9/5

(81)

Question 248

Solve the equation. - $7 x ^ { 2 } + 21 x + 14 = 0$

(Multiple Choice)

4.9/5

(74)

Question 249

Factor the perfect square trinomial completely. - $x ^ { 2 } - 10 x + 100$

(Multiple Choice)

4.8/5

(75)

Question 250

Find a positive value of the given variable so that the trinomial is factorable. - $11 x ^ { 2 } + b x + 1 ; b = \text { ? }$

(Multiple Choice)

4.9/5

(73)

Question 251

Factor the four-term polynomial by grouping. - $15 x ^ { 2 } - 10 x y - 18 x y + 12 y ^ { 2 }$

(Multiple Choice)

4.9/5

(75)

Question 252

Factor the sum or difference of two cubes. - $54 x ^ { 3 } y ^ { 6 } - 50 x ^ { 6 } y ^ { 3 }$

(Multiple Choice)

4.8/5

(69)

Question 253

Factor the perfect square trinomial completely. - $z ^ { 2 } + 4 z + 4$

(Multiple Choice)

4.7/5

(88)

Question 254

Fill in the blank with one of the words or phrases listed below. Not all choices will be used and some choices may be used more than once. factoring quadratic equation perfect square trinomial 0 greatest common factor hypotenuse sum of two cubes 1 difference of two cubes difference of two squares triangle leg -The expression $a ^ { 2 } - b ^ { 2 }$ is called a_______

(Multiple Choice)

4.7/5

(85)

Question 255

Factor out the GCF from the polynomial. - $s \left( t ^ { 2 } + 11 \right) - 3 \left( t ^ { 2 } + 11 \right)$

(Multiple Choice)

4.9/5

(66)

Question 256

Solve. - $\text { A triangle is } 8 \mathrm {~cm} \text { wider than it is tall. The area is } 280 \mathrm {~cm} ^ { 2 } \text {. Find the width (length of the base). }$ $Solve. - \text { A triangle is } 8 \mathrm {~cm} \text { wider than it is tall. The area is } 280 \mathrm {~cm} ^ { 2 } \text {. Find the width (length of the base). }$

(Multiple Choice)

4.8/5

(79)

Question 257

Fill in the blank with one of the words or phrases listed below. Not all choices will be used and some choices may be used more than once. factoring quadratic equation perfect square trinomial 0 greatest common factor hypotenuse sum of two cubes 1 difference of two cubes difference of two squares triangle leg -In a right triangle, the side opposite the right angle is called the ________

(Multiple Choice)

4.8/5

(83)

Question 258

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $6 t ^ { 2 } + t - 5$

(Multiple Choice)

4.8/5

(83)

Question 259

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 2 } + x - 56$

(Multiple Choice)

4.9/5

(79)

Question 260

Solve. -Within a group of $\mathrm { n }$ people, the number of possible handshakes, $N$ , is given by $\mathrm { N } = \frac { 1 } { 2 } \left( \mathrm { n } ^ { 2 } - \mathrm { n } \right)$ . How many handshakes are possible at a meeting if 16 people are present?

Factor completely. - $12 x ^ { 2 } + 17 x + 6$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $2 x ^ { 2 } - 19 x + 45$

Factor out the GCF from the polynomial. - $28 m ^ { 8 } - 8 m ^ { 6 } + 28 m ^ { 4 }$

Solve. -Two vehicles leave the same corner at the same time and travel at a right angle to each other. One vehicle travels 2 kilometers an hour faster than the other. If after one hour the vehicles are 10 kilometers apart, find the rate of each vehicle.

Factor completely. - $9 x ^ { 2 } + x - 140$

Factor the sum or difference of two cubes. - $512 - t ^ { 3 }$

Solve the equation. - $x ^ { 2 } + 5 x - 36 = 0$

Solve the equation. - $7 x ^ { 2 } + 21 x + 14 = 0$

Factor the perfect square trinomial completely. - $x ^ { 2 } - 10 x + 100$

Find a positive value of the given variable so that the trinomial is factorable. - $11 x ^ { 2 } + b x + 1 ; b = \text { ? }$

Factor the four-term polynomial by grouping. - $15 x ^ { 2 } - 10 x y - 18 x y + 12 y ^ { 2 }$

Factor the sum or difference of two cubes. - $54 x ^ { 3 } y ^ { 6 } - 50 x ^ { 6 } y ^ { 3 }$

Factor the perfect square trinomial completely. - $z ^ { 2 } + 4 z + 4$

Factor out the GCF from the polynomial. - $s \left( t ^ { 2 } + 11 \right) - 3 \left( t ^ { 2 } + 11 \right)$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $6 t ^ { 2 } + t - 5$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 2 } + x - 56$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 6: Factoring Polynomials

Solve. -Within a group of n\mathrm { n }n people, the number of possible handshakes, NNN , is given by N=12(n2−n)\mathrm { N } = \frac { 1 } { 2 } \left( \mathrm { n } ^ { 2 } - \mathrm { n } \right)N=21​(n2−n) . How many handshakes are possible at a meeting if 16 people are present?

Factor completely. - 12x2+17x+612 x ^ { 2 } + 17 x + 612x2+17x+6

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - 2x2−19x+452 x ^ { 2 } - 19 x + 452x2−19x+45

Factor out the GCF from the polynomial. - 28m8−8m6+28m428 m ^ { 8 } - 8 m ^ { 6 } + 28 m ^ { 4 }28m8−8m6+28m4

Solve. -Two vehicles leave the same corner at the same time and travel at a right angle to each other. One vehicle travels 2 kilometers an hour faster than the other. If after one hour the vehicles are 10 kilometers apart, find the rate of each vehicle.

Factor completely. - 9x2+x−1409 x ^ { 2 } + x - 1409x2+x−140

Factor the sum or difference of two cubes. - 512−t3512 - t ^ { 3 }512−t3

Solve the equation. - x2+5x−36=0x ^ { 2 } + 5 x - 36 = 0x2+5x−36=0

Solve the equation. - 7x2+21x+14=07 x ^ { 2 } + 21 x + 14 = 07x2+21x+14=0

Factor the perfect square trinomial completely. - x2−10x+100x ^ { 2 } - 10 x + 100x2−10x+100

Find a positive value of the given variable so that the trinomial is factorable. - 11x2+bx+1;b= ? 11 x ^ { 2 } + b x + 1 ; b = \text { ? }11x2+bx+1;b= ?

Factor the four-term polynomial by grouping. - 15x2−10xy−18xy+12y215 x ^ { 2 } - 10 x y - 18 x y + 12 y ^ { 2 }15x2−10xy−18xy+12y2

Factor the sum or difference of two cubes. - 54x3y6−50x6y354 x ^ { 3 } y ^ { 6 } - 50 x ^ { 6 } y ^ { 3 }54x3y6−50x6y3

Factor the perfect square trinomial completely. - z2+4z+4z ^ { 2 } + 4 z + 4z2+4z+4

Factor out the GCF from the polynomial. - s(t2+11)−3(t2+11)s \left( t ^ { 2 } + 11 \right) - 3 \left( t ^ { 2 } + 11 \right)s(t2+11)−3(t2+11)

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - 6t2+t−56 t ^ { 2 } + t - 56t2+t−5

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - x2+x−56x ^ { 2 } + x - 56x2+x−56

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Solve. -Within a group of $\mathrm { n }$ people, the number of possible handshakes, $N$ , is given by $\mathrm { N } = \frac { 1 } { 2 } \left( \mathrm { n } ^ { 2 } - \mathrm { n } \right)$ . How many handshakes are possible at a meeting if 16 people are present?

Factor completely. - $12 x ^ { 2 } + 17 x + 6$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $2 x ^ { 2 } - 19 x + 45$

Factor out the GCF from the polynomial. - $28 m ^ { 8 } - 8 m ^ { 6 } + 28 m ^ { 4 }$

Factor completely. - $9 x ^ { 2 } + x - 140$

Factor the sum or difference of two cubes. - $512 - t ^ { 3 }$

Solve the equation. - $x ^ { 2 } + 5 x - 36 = 0$

Solve the equation. - $7 x ^ { 2 } + 21 x + 14 = 0$

Factor the perfect square trinomial completely. - $x ^ { 2 } - 10 x + 100$

Find a positive value of the given variable so that the trinomial is factorable. - $11 x ^ { 2 } + b x + 1 ; b = \text { ? }$

Factor the four-term polynomial by grouping. - $15 x ^ { 2 } - 10 x y - 18 x y + 12 y ^ { 2 }$

Factor the sum or difference of two cubes. - $54 x ^ { 3 } y ^ { 6 } - 50 x ^ { 6 } y ^ { 3 }$

Factor the perfect square trinomial completely. - $z ^ { 2 } + 4 z + 4$

Factor out the GCF from the polynomial. - $s \left( t ^ { 2 } + 11 \right) - 3 \left( t ^ { 2 } + 11 \right)$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $6 t ^ { 2 } + t - 5$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 2 } + x - 56$