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Polynomial Functions. Quiz Show. (11x 5 + 7x 4 – 5x 3 ) + (12x 6 + 6x 4 – 8x). 100A. (3x 2 + 7x – 4) – (10x 2 + 15x + 7). 100B. Multiply (3 x 2 + 2 x + 5) by (5 x + 6). 100C.

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Polynomial Functions

Quiz Show


(11x 5 + 7x 4 – 5x 3) + (12x 6 + 6x 4 – 8x)

100A


(3x 2 + 7x – 4) – (10x 2 + 15x + 7)

100B


Multiply (3 x 2 + 2 x + 5) by (5 x + 6)

100C


Divide (2x 4 – 15x 2 – 10x + 5) by (x – 3) using long division

100D


Divide (x 3 + 5x 2 – 8x + 28) by (5 x – 1) using synthetic division

100E


Evaluate f(x) = 3 x 2 – 5 x + 6 for f(2i)

200A


Evaluate f(x) = 8 x – 4 x 2for f(1 - )

200B


If f(x) = 4x 3 – 5x 2 + 7x- 9, use synthetic substitution to find f(2)

200C


If f(x) = 4x 3 – 5x 2 + 7x- 9, use synthetic substitution to find f(- 3)

200D


If f(x) = 3x3 – 7x2 + 2x+ 3, use synthetic substitution to find f( )

200E


Factorx 3 – 1000

300A


Factorx 4 – 7x 2 – 8

300B


Factor64 – 125x3

300C


Solve3x4 + 12x2 – 15= 0

300D


Solvex3 – 5x2 + 4x– 20 = 0

300E


A rectangle has a perimeter of 80 cm. If its width is x, express its area in terms of x. What is the maximum area of the rectangle?

400A


The volume of a box is given by V(x) = x(10 – x)(10 – 2x). Find the approx. max. volume.

400B


An open box is to be formed by cutting squares from a square sheet of 10 cm on each side. Find the value of x that maximizes the volume.

400C


A polynomial equation with rational coefficients has the given roots. Find 2 additional roots.– and 5 +

400D


A polynomial equation with rational coefficients has the given roots. Find 2 additional roots.– 7i and 3 + 7i

400E


Sketch an approx. graph of y = x 6

500A


Determine the max. number of zeros and vertices of the polynomial P(x) = 12x 6 + 6x 4 – 8x

500B


Given the polynomial P(x) = (x – 5) (x + 6) 4, where is the graph tangent and where does it cross the x-axis?

500C


Given the polynomial P(x) = – 5x 2 + 7x– 9, describe the behavior of the graph on the right and left

500D


Sketch the graph of f(x) = (x + 1)(x – 1)(x – 2)

500E


(11x 5 + 7x 4 – 5x 3) + (12x 6 + 6x 4 – 8x)

12x 6 + 11x 5 + 13x 4 – 5x 3 – 8x

100A


(3x 2 + 7x – 4) – (10x 2 + 15x + 7)

- 7x 2 – 8x – 11

100B


Multiply (3 x 2 + 2 x + 5) by (5 x + 6)

12x 6 + 11x 5 + 13x 4 – 5x 3 – 8x

100C


Divide (2x 4 – 15x 2 – 10x + 5) by (x – 3) using long division

Q: 2x 3 + 6x 2 + 3x – 1R: 2

100D


Divide (x 3 + 5x 2 – 8x + 28) by (5 x – 1) using synthetic division

Q: x 2 + 3x – 1R: 0

100E


Evaluate f(x) = 3 x 2 – 5 x + 6 for f(2i)

- 2 – 10i

200A


Evaluate f(x) = 8 x – 4 x 2for f(1 - )

- 4

200B


If f(x) = 4x 3 – 5x 2 + 7x- 9, use synthetic substitution to find f(2)

17

200C


If f(x) = 4x 3 – 5x 2 + 7x- 9, use synthetic substitution to find f(- 3)

- 183

200D


If f(x) = 3x3 – 7x2 + 2x+ 3, use synthetic substitution to find f( )

3

200E


Factorx 3 – 1000

(x2-10)(x+10x+100x2)

300A


Factorx 4 – 7x 2 – 8

(x2-8)(x2+1)

300B


Factor64 – 125x3

(4 – 5x) (16 + 20x + 25x2)

300C


Solve3x4 + 12x2 – 15= 0

x = 1; x = - 1; x =

300D


Solvex3 – 5x2 + 4x– 20 = 0

x = 2; x = - 2; x = 5

300E


A rectangle has a perimeter of 80 cm. If its width is x, express its area in terms of x. What is the maximum area of the rectangle?

x(40 – x); 400 cm 2

400A


The volume of a box is given by V(x) = x(10 – x)(10 – 2x). Find the approx. max. volume.

x = 1.67; 9.26 ft 3

400B


An open box is to be formed by cutting squares from a square sheet of 10 cm on each side. Find the value of x that maximizes the volume.

x = 1.7; 74.1 cm 3

400C


A polynomial equation with rational coefficients has the given roots. Find 2 additional roots.– and 5 +

and 5 –

400D


A polynomial equation with rational coefficients has the given roots. Find 2 additional roots.– 7i and 3 + 7i

7i and 3 – 7i

400E


Sketch an approx. graph of y = x 6

500A


Determine the max. number of zeros and vertices of the polynomial P(x) = 12x 6 + 6x 4 – 8x

6 zeros; 5 vertices

500B


Given the polynomial P(x) = (x – 5) (x + 6) 4, where is the graph tangent and where does it cross the x-axis?

Tangent @ - 6; crosses @ 5

500C


Given the polynomial P(x) = – 5x 2 + 7x– 9, describe the behavior of the graph on the right and left

Rises to the left & falls to the right

500D


Sketch the graph of f(x) = (x + 1)(x – 1)(x – 2)

x = -1; x = 1; x = 2(1.5, -.625); (0, 2); (-2, -12)

500E


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