Unit 4: Polynomial Functions

Adding, Subtract, and Multiplying

100

(5x³ + 2x² - 11) + (7x² - 6x + 4)

5x³ + 9x² - 6x - 7

200

(6x² + 5x + 4) - (3x² - 4x + 8)

3x² + 9x - 4

300

(x³ - 3x² + 7) - (x⁴ + 2x³ + 8x)

-x⁴ - x³ - 3x² - 8x + 7

400

(2x + 5)(x² + x - 1)

2x³ + 7x² + 3x -5

500

(3x-2)³

27x³ - 54x² + 36x - 8

Dividing Polynomials

100

(x² + x - 2) ÷ (x - 1) 

(x + 2)

200

Image question - A

(3x³ + 4x² - 5) ÷ (x + 2)

300

Image Question - B

-13

400

The remainder when (x³ - 2x² - 2x + 8) is divided by (x - 1)

5

500

Is (x - 1) a factor of (x⁴ + x³ - 25x² - 37x + 60) ?

Yes! When we divide the polynomial by (x - 1), the remainder is 0.

End Behavior

100

Sketch the end behavior of f(x) = -4x³ + 2x² - 3x + 12.

[picture]

200

Sketch the end behavior of g(x) = -4x⁴ + 2x² - 3x + 12.

[picture]

300

For the function f(x) = 4x³ + 3x² - 3x - 21, as x -> ∞, f(x) approaches this.

∞ (positive infinity)

400

For the function f(x) = -6x⁶ + 9x⁵ - 3x³ - 21, as x -> -∞, f(x) approaches this.

- ∞

500

Sketch the end behavior for the function represented by k(x) = (x - 2)(x+3)(x - 4)²

[drawing]

Factoring & Solving

100

The solutions to the factored function (x + 2)(x - 3)(x²)

x = -2, x = 3, x = 0

200

The solutions to the factored function g(x) = (x² + 3)(x - 4)(x + 4)

x = 4, x = -4

The first factor has no solution.

300

factor x³ + 10x² + 21x completely

x (x + 3) (x + 7)

400

Factor 5x⁷ - 125x⁵ completely.

5x⁵(x - 5)(x + 5)

500

Factor completely: m(x) = 8x³ + 27

(2x + 3)(4x² - 6x + 9)

Misc.

100

The behavior of the graph h(x) = (x - 2)² (x + 3) at the x intercept of 2.

bounce

200

The shape that a quadratic function makes on a graph

parabola

300

The concert that Katherine has been saving all her $$$ for.

Beyonce

400

The behavior of the graph g(x) = (x - 4)⁵ (x + 9) at the x intercept of 4.

Wiggle/squiggle/flatten out

500

To factor a binomial a³ - b^3, use this formula.

(a - b)(a² + ab + b²)