# Math 4 Unit 3: Polynomials

Completely factor x^2+6x+8

= (x+4)(x+2)

Completely factor 3x^2+4x-7

= (3x+7)(x-1)

Completely factor

= x^2(x-7) – 3(x-7)

= (x^2-3)(x-7)

#### Factoring Quartics

Completely factor 2x^4-28x^2+90

= 2(x^4-14x^2+45)

= 2(x^2-9)(x^2-5)

= 2(x+3)(x-3)(x^2-5)

#### Solving Quartics

Completely factor.

= 2x^4-28x^2+90

= 2(x^4-14x^2+45)

= 2(x^2-9)(x^2-5)

= 2(x+3)(x-3)(x^2-5)

x=-3, 3, +-sqrt 5

#### Vertex Form

Rewrite in vertex form.

#### Graphing Polynomials

• Determine the End Behavior based on the Leading Coefficient Test and write the end behavior of this polynomial in Limit Notation.
• Find the zeros of the polynomial function
• Find the y-intercept of the polynomial function
• Graph the polynomial function.

#### Write a Polynomial with Roots

Find a polynomial function with the given zeros: 0, 2 mult 2

#### Long Division

Divide with Long Division

#### Synthetic Division

Divide with Synthetic Division

#### Rational Roots Theorem

Use the Rational Roots Theorem to find all possible roots and then solve.