Exam 5: Polynomials and Polynomial Functions

Solve the problem. -The volume of a sphere is a function of its radius, r, where $\mathrm { V } ( \mathrm { r } ) = \frac { 4 } { 3 } \pi \mathrm { r } ^ { 3 }$ . Find the volume of a sphere if its radius is 7 inches. Use 3.14 as an approximation to the value of π. Round to the nearest tenth if necessary.

Give the degree of the polynomial and identify its leading coefficient. - $- 9 x ^ { 4 } - 7 w ^ { 3 } + 2 w - 4 y ^ { 5 } + 4$

Determine which of the graphs is the graph of the equation. - $f ( x ) = 8 x ^ { 3 } + 2 x ^ { 2 } - 4 x + 2$

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. - $- 10 a ^ { 2 }$

Simplify. - $6 z - ( 17 - 2 z )$

Multiply the polynomials. - $( 6 y + 11 ) \left( 2 y ^ { 2 } - 2 y - 4 \right)$

Multiply. - $\left( q + \frac { 4 } { 3 } \right) \left( q + \frac { 3 } { 4 } \right)$

Determine which of the graphs is the graph of the equation. - $f ( x ) = 4 x ^ { 2 } - 2 x - 1$

Find an expression for the perimeter of the figure. -

Simplify. -( $\left( 4 x ^ { 2 } - 2 x - 1 \right) - \left( 2 x ^ { 2 } + 6 x - 4 \right)$

Multiply. - $\left( - 7 x ^ { 5 } y \right) \left( - 4 x ^ { 6 } y ^ { 3 } \right)$

Simplify. - $\left( 12 x ^ { 2 } y - 6 x y + 9 \right) + \left( - 11 x ^ { 2 } y + 8 x y - 5 \right)$

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state. Give the degree of the polynomial. - $3 x y ^ { 3 } - 2 x ^ { 2 } + 9 + 11 x ^ { 3 }$

Simplify. - $( 18 y + 5 ) - \left( - 14 y ^ { 2 } - 9 y + 5 \right)$

Evaluate the polynomial function at the given value. -Findd P( $P ( - 5 ) \text { if } P ( x ) = 2 x ^ { 2 } - 9 x - 6$

Multiply. - $\frac { 1 } { 3 } y z \left( 2 x + 7 y ^ { 2 } + 8 y \right)$

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial, binomial, or trinomial. If the expression is not a polynomial, indicate why not. --15x

Multiply. - $\left( \frac { 2 } { 7 } x + 6 \right) \left( \frac { 1 } { 2 } x - 1 \right)$

Multiply. -( $( 6 x - 4 ) \left( 2 x ^ { 2 } - 3 \right)$

Evaluate the polynomial function at the given value. -Find P(-1)if P(x)= $x ^ { 2 } + 8$