Exam 5: Polynomials and Polynomial Functions

Solve the problem. -The number of ways that the first-, second-, and third-place winners in a singing competition can be selected from n finalists is given by $P ( n ) = n ^ { 3 } - 3 n ^ { 2 } + 2 n$ . If there are6 finalists, how many ways can the first-, second-, And third-place winners be selected?

Simplify. -Subtract ( $\left( 12 a ^ { 2 } b - 9 a b \right)$ from ( $\left( 10 a ^ { 2 } b - 13 a b \right)$

Solve the problem. -Computer sales in the United States have increased since 1992. The function $f ( x ) = 0.058 x ^ { 2 } + 0.69 x + 4.8$ can be used to approximate the number of computer sales during the years 1990-2000 where x is the number of years After 1990 and f(x)is the computer sales (in millions). Approximate the number of computers sold in 1996. Round the answer to the nearest tenth of a million.

Multiply. - $( 6 x - 5 y ) ( 7 x - 9 y )$

Simplify. - $\left( 7 x ^ { 2 } - x y - y ^ { 2 } \right) + \left( x ^ { 2 } + 6 x y - 5 y ^ { 2 } \right)$

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. - $- 1 - 3 x ^ { 4 } + 7 x ^ { 5 }$

Solve the problem. -The polynomial $- 0.3 \mathrm { t } ^ { 2 } + 10 \mathrm { t }$ describes the average number of digits that participants in a memorization experiment were able to recall after t minutes. Find the number of digits recalled after 9 minutes. Round to the Nearest digit.

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. - $- 11 z + 6$

Solve the problem. -The total cost in dollars for a certain company to produce x empty jars to be used by a jelly producer is given by the polynomial equation C(x)= 0.6x + 27,000. Find the cost of producing 90,000 jars.

Simplify. - $\left[ \left( 1.9 x ^ { 3 } + 7.4 x ^ { 2 } + 4.7 \right) + ( 6.5 x - 2.8 ) \right] - \left( 3.9 x ^ { 2 } - x - 9.6 \right)$

Multiply. Assume that all variables represent natural numbers. - $\left( x ^ { 2 n } - y \right) \left( x ^ { 3 n } - 6 y ^ { 2 n } \right)$

Simplify. -Subtract (x - 2)from (8x - 4)

Solve the problem. -The distance in feet it takes a car traveling at x mph to come to a full stop after hitting the brakes is given by $1.28 \mathrm { x } ^ { 2 } + 0.056 \mathrm { x }$ Find the stopping distance for a speed of 40 mph. Round to the nearest foot.

Multiply. -(x - 4y)(x - 11y)

Multiply. -(2x + 5)(x + 6)

Give the degree of the polynomial and identify its leading coefficient. - $8 x ^ { 3 } y ^ { 2 } - 7 x ^ { 5 } y ^ { 4 } + x ^ { 9 } y$

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. - $- 10 y ^ { 4 } - 9$

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

Multiply. - $0.8 x ^ { 2 } y ^ { 2 } \left( 2.2 x ^ { 5 } y - 4.9 x ^ { 3 } y ^ { 2 } + 1.9 x y ^ { 3 } \right)$

Solve the problem. -The volume of a cube is a function of its side, s, where $V ( s ) = s ^ { 3 }$ . Find the volume of a cube if its side is 9 centimeters.