Exam 5: Polynomials, Polynomial Functions, and Factoring

Add the polynomials. Assume all variable exponents represent whole numbers. - $\left( 12 x ^ { 5 } y ^ { 3 } + 10 x ^ { 3 } y ^ { 2 } + 2 x y \right) + \left( 4 x ^ { 5 } y ^ { 3 } + 5 x ^ { 3 } y + 3 x y \right)$

Multiply the monomials. Assume any variable exponents represent whole numbers. - $\left( 3 x ^ { 4 } y \right) \left( - 6 x ^ { 7 } y ^ { 2 } \right)$

Multiply the monomial and the polynomial. Assume any variable exponents represent whole numbers. - $4 x ^ { n } \left( 2 x ^ { 3 n } + 3 x ^ { n } + \frac { 1 } { 4 } x \right)$

Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers. - $( x + 4 ) ( x + 1 )$

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers. - $\left( 5 a ^ { n } + 4 \right) \left( 5 a ^ { n } - 4 \right)$

Subtract the polynomials. Assume all variable exponents represent whole numbers. - $\left( 3 x ^ { 6 } - 15 x ^ { 3 } - 11 \right) - \left( 9 x ^ { 6 } - 20 x ^ { 3 } + 3 \right)$

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers. - $12 x ^ { 3 n } - 30 x ^ { 2 n }$

Find the product. Assume all variable exponents represent whole numbers. - $( x + 6 ) \left( x ^ { 2 } + 3 x - 2 \right)$

Use the graph to estimate the average number of minutes a woman exercised per week if her average monthly weight loss was 4.4 pounds. A) 115 min B) 120 min C) 135 min D) 127 min Answer: B Determine whether the graph shown is the graph of a polynomial function. -

Multiply the monomial and the polynomial. Assume any variable exponents represent whole numbers. - $5 x y ( 3 x - 9 y )$

Solve the problem. -A herd of bison is introduced to a wildlife refuge. The number of bison, $\mathrm { N } ( \mathrm { t } )$ , after $t$ years is described by the polynomial function $N ( t ) = - t ^ { 4 } + 23 t + 120$ . Use the Leading Coefficient Test to determine the graph's end behavior. What does this mean about what will eventually happen to the bison population?

Use the FOIL method to multiply the binomials. Assume any variable exponents represent whole numbers. - $( 8 x + 12 y ) ( 8 x - 10 y )$

Give the requested components for the polynomial. - $\mathrm { x } ^ { 5 } - 10 \mathrm { x } ^ { 2 }$ ; the degree of each term and the coefficient of each term

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers. - $\left( 10 x ^ { 2 } - 3 y \right) ^ { 2 }$

Given the polynomial functions, find the product function and the specified value. -Let $f ( x ) = x + 3$ and $g ( x ) = x ^ { 2 } - 9 x - 7$ . Find $( f g ) ( x )$ and $( f g ) ( - 4 )$ .

Find the product. Assume all variable exponents represent whole numbers. - $( x + y ) \left( x ^ { 2 } - 6 x y - y ^ { 2 } \right)$

Multiply the monomial and the polynomial. Assume any variable exponents represent whole numbers. - $6 y \left( 5 y ^ { 2 } - 11 y \right)$

Use the graph to estimate the average number of minutes a woman exercised per week if her average monthly weight loss was 4.4 pounds. A) 115 min B) 120 min C) 135 min D) 127 min Answer: B Determine whether the graph shown is the graph of a polynomial function. -

Multiply using one of the rules for the square of a binomial. Assume any variable exponents represent whole numbers. - $( 7 x - y ) ^ { 2 }$

Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers. - $( x - y + 4 ) ( x - y - 4 )$