Exam 5: Polynomials and Polynomial Functions

Simplify. - $\left( - \frac { 1 } { 3 } x ^ { 2 } + \frac { 3 } { 4 } x - \frac { 2 } { 5 } \right) + \left( - \frac { 1 } { 4 } x ^ { 2 } + \frac { 4 } { 5 } x + \frac { 1 } { 2 } \right)$

Multiply. - $\frac { 4 } { 9 } w ^ { 6 } \left( 2 w ^ { 8 } + 2 w ^ { 6 } - \frac { 5 } { 4 } \right)$

Solve the problem. -When a coin is dropped from a cliff of height 1800 feet, the height h of the coin from the ground (in feet)t seconds after being dropped is given by h = $- 16 t ^ { 2 }$ + 1800. How high is the coin above the ground 9 seconds After being dropped?

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. - $- 20 x ^ { 7 } + 9$

Give the degree of the polynomial and identify its leading coefficient. - $\frac { 8 } { 15 } m ^ { 3 } n ^ { 2 } p ^ { 4 } - m ^ { 6 } p ^ { 2 } - \frac { 5 } { 13 } m n ^ { 3 } p ^ { 6 }$

Simplify. -Subtract $- 7 s ^ { 2 } - 3 s + 1 . \text { from } - s ^ { 2 } - 7 s + 5$

Simplify. Assume that all exponents represent natural numbers. - $\left( 3 y ^ { 2 n } + 9 y ^ { n } - 1 \right) - \left( 4 y ^ { 2 n } + 3 y ^ { n } - 9 \right)$

Multiply. Assume that all variables represent natural numbers. - $- 9 k ^ { r + 1 } \left( 7 k ^ { r + 4 } - 4 k ^ { r + 3 } - 6 k \right)$

Multiply. - $7 z ^ { 2 } \left( 7 z ^ { 2 } + 7 z - 6 \right)$

Solve the problem. -An object is thrown upward with an initial velocity of 20 feet per second from the top of a 588-foot building. The height of the object at any time t can be described by the polynomial function $P ( t ) = - 16 t ^ { 2 } + 20 t + 588$ F Find The height of the object at t = 5 seconds.

Multiply. - $7 x ^ { 2 } \left( - 12 x ^ { 7 } - 7 x ^ { 4 } - 9 \right)$

Evaluate the polynomial function at the given value. -Find P(0.2)if P(x)= $0.2 x ^ { 2 }$ - 4.2x + 2.7

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. - $5 x - 6 x ^ { 3 } + 1$

Multiply. - $0.4 ( 2.2 \mathrm { a } - 4.7 \mathrm {~b} + 1.6 \mathrm { c } )$

Simplify. - $\left( 5 m ^ { 2 } + 9 m n - 6 n ^ { 2 } \right) - \left( 9 m ^ { 2 } + 4 m n - 9 n ^ { 2 } \right)$

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. - $4 x ^ { 3 } + 5 x ^ { 2 } - 4 x ^ { - 4 }$

Evaluate the polynomial function at the given value. -Find P(-2)if P(x)= -9x - 8.

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. -7

Find an expression for the perimeter of the figure. - $x ^ { 2 } - 9 x + 1$

Multiply the polynomials. - $( x - 11 ) \left( x ^ { 2 } + 7 x - 5 \right)$