Polynomials and Polynomial Functions

Sketch the Graph

100

Sketch the graph of:

f(x) = (x+4)(x+4)

even/positive

one tangent x-intercept at x = -4

200

Sketch:

g(x) = -(x+3)(x-2)

even/negative

one x-intercept at x = -3, 2

300

Sketch:

f(x) = (x+4)(x-1)(x-8)

odd/positive

x-intercepts at -4, 1, 8

400

Sketch the graph:

f(x) = x(x²-4)

odd/positive

three x-intercepts: -2, 0, 2

500

Sketch:

j(x) = -(x² - 9)(x + 1)

odd/negative

three x-intercepts: -3, -1, 3

Polynomial Factors and Zeros

100

Find the zeros of the function: y = (x - 3)(x + 2)

{-2, 3}

200

Write the polynomial in factored form: x³ + 7x² + 10x

x(x + 5)(x + 2)

300

Find the zeros of the function: y = x(x + 1)(x - 7)

{-1, 0, 7}

400

Write a polynomial function, that opens up, in factored form with the given zeros: 5, 4

y = (x-5)(x-4)

500

Write a polynomial function, that has a positive leading coefficient, in factored form with the given zeros: 1, -1, -2

y = (x-1)(x+1)(x+2)

Dividing Polynomials

100

Find the quotient of 6t³ +15t² -15t divided by -3

-2t³ -5t² +5t

200

Find the quotient: (x² + 10x + 21) ÷ (x + 3)

x + 7

300

Find the quotient and remainder: (2x² + 7x + 8) ÷ (x + 2)

Quotient: 2x + 3, remainder: 2

400

Find the quotient and remainder: (x³ + 3x² - x + 2) ÷ (x - 1)

Quotient: x² + 4x + 3, remainder: 5

500

Find the quotient and remainder: (x³ + 11x + 12) ÷ (x + 3)

Quotient: x² - 3x + 20, remainder: -48

Function Operations

100

What is (f + g) (x)?

f(x)= 2x² - x

g(x)= x²

What is 3x² - x ?

200

What is (f/g) (x)?

f(x) = -5x +6

g(x)=-2x

-5x+6/-2x, x =\ 0

300

What is (f x g)(x)?

f(x) = 5x + 4

g(x) = 4x +1 

20x² +21x + 4

400

What is (f - g) (x)?

f(x) = -3x

g(x) = x² + 7x

- 4x² + 7x