Exam 5: Polynomials and Polynomial Functions

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. - $- 10 x - 6$

Solve the problem. -Total profit is defined as total revenue minus total cost. R(x)is the revenue from the sale of x televisions and C(x)is the cost of producing x televisions.(x)is the cost of producing x televisions. $\text { If } R ( x ) = 240 x - 0.7 x ^ { 2 } \text { and } C ( x ) = 4000 + 0.6 x ^ { 2 } \text {, }$ find the profit from the Sale of 80 televisions.

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. - $- 8 x ^ { 3 } - 2 x ^ { 4 } + 8 x ^ { 5 } + 12$

Multiply. -(x - 6)(4x + 7)

Simplify. - $\left( 10 a ^ { 2 } b - 12 a b + 8 \right) - \left( 2 a ^ { 2 } b + 2 a b - 4 \right)$

Multiply. - $\left( \frac { 12 } { 5 } a ^ { 2 } b ^ { 3 } \right) \left( \frac { 1 } { 9 } a b ^ { 4 } c \right)$

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. - $x ^ { 4 / 3 } - x ^ { 6 } - 1$

Multiply. - $( 0.7 a + b ) \left( 2.6 a ^ { 2 } - 4.8 b \right)$

Multiply. - $( - 5 x y ) \left( - 2 x y ^ { 2 } \right)$

Solve the problem. -A projectile is fired upward from the ground with an initial velocity of 300 feet per second. Neglecting air resistance, the height of the projectile at any time t can be described by the polynomial function $P ( t ) = - 16 t ^ { 2 } + 300 t$ . Find the height of the projectile at t = 8 seconds.

Multiply. - $\frac { 1 } { 5 } x ^ { 2 } y ^ { 4 } ( 4 x - 7 y - 8 )$

Give the degree of the polynomial and identify its leading coefficient. - $- 9 x ^ { 3 } + 8 x ^ { 4 } - x ^ { 5 } + 12$

Evaluate the polynomial function at the given value. - $\text { Find } \mathrm { P } \left( \frac { 1 } { 2 } \right) \text { if } \mathrm { P } ( \mathrm { x } ) = - 2 \mathrm { x } ^ { 2 } + 5 \mathrm { x } + 7$

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. - $6 y ^ { 5 } + 8 y ^ { 4 } - 6$

Simplify. - $( 14 y + 2 ) - \left[ - 6 y ^ { 2 } - ( 7 y - 2 ) \right]$

Multiply. -(1.8x - 6y)(3.2x + 9y)

Multiply. - $- 6 x ^ { 2 } y \left( 6 x ^ { 2 } y ^ { 4 } + 4 x y ^ { 3 } - 11 \right)$

Solve the problem. -The number of different committees of 2 students where the 2 students are selected from a group of n students is given by $c ( n ) = \frac { 1 } { 2 } \left( n ^ { 2 } - n \right)$ n). How many different committees of 2 students can be selected from a group of 10 Students?

Multiply. Assume that all variables represent natural numbers. - $\left( x ^ { a } + 7 \right) \left( x ^ { 2 a } + 3 \right)$

Find an expression for the perimeter of the figure. - $~~~~~~x^{2}-x+17$