5.4 Factor and Solve Polynomial Functions SWBAT Factor and Solve Polynomial Functions

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?