5.4 Factor and Solve Polynomial Functions

SWBAT Factor and Solve Polynomial Functions

General Rules for Factoring Polynomials 1) Is there a common monomial? 2) General Trinomial? 3) Perfect Square Trinomial? 4) Difference of 2 squares?

General Rules for Factoring Polynomials continued 5) Difference of Cubes? 6) Sum of Cubes?

We will talk more about #5 and #6 later.

Factor completely means it is written as a product of unfactorable polynomials with integer coefficients.

Factor completely:

Special cases of factoring cubes. Sum of cubes: Difference of cubes:

Factor

Factoring by grouping, (we did this in the never fail method).

𝑥2(𝑥−3)−16 (𝑥−3)(𝑥2−16 ) (𝑥−3)

(𝑥−4)(𝑥+4)(𝑥−3)

Factoring by grouping.

Factor:

Factor completely, with respect to real numbers:

3

10(𝑥4−1)10(𝑥2−1)(𝑥2+1)

10(𝑥−1)(𝑥+1)(𝑥2+1)

3𝑚2(𝑚10+18𝑚5+17)3𝑚2(𝑚5+1)(𝑚5+17)

Find Solutions:

2 𝑥5=12𝑥3−16 𝑥1. Set equal to zero,

2. Common Monomial? 2 𝑥(𝑥4−6𝑥2+8)3. Any more factoring? 2 𝑥(𝑥2−4 )(𝑥2−2)

2 𝑥(𝑥−2)(𝑥+2)(𝑥2−2)4. Any more factoring?

5. Any more factoring?

6. Set all factors = to 0 and solve them all.

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Questions?