FACTORING POLYNOMIALSHonors Advanced Algebra

Presentation 2-5

Warm-Up

•Solve using synthetic division

Factoring ReviewGCF (Greatest Common Factor)• Look for the largest number that divides evenly into each

term.

• Look at each term, for each variable, take out the smallest exponent of that variable of all of the terms.

• Example 1:

• Example 2:

Factoring ReviewTrinomial where a = 1• Identify your coefficient b and your constant c.

• Find 2 factors of c that add to give you b.

• Example 1:

• Example 2:

Factoring ReviewGrouping• Put parentheses around the first 2 and second 2 terms.

Include any negative sign in the parentheses.

• Take out the GCF of each set of binomials. You should end up with the same binomial remaining in the parentheses.

• Group the GCFs as one binomial and the common binomial as the second.

• Example 1:

• Example 2:

Factoring ReviewTrinomial where a > 1• Identify your coefficient b and the product of a and c.

• Find 2 factors for a*c that add to give you b.

• Rewrite the middle term using these factors and factor by grouping.

• Example 1:

• Example 2:

Difference of Squares

• Example 1:

• Example 2:

• Example 2:

Perfect Cubes

•Exponents that are a multiple of 3

Factors of a Polynomial

• A linear binomial is a factor of a polynomial if it divides into the polynomial with a remainder of 0.

Example: Is (x – 4) a factor of (5x3 – 20x2 + 4x – 16)

• A factor of a polynomial will result in an x-intercept on a graph at the intercept (c, 0) for a factor (x – c) or (ax – ac).

Example: Find the x-intercept of a graph that has a factor of (2x – 6).

Sum or Difference of Two Cubes

• Example 1:

• Example 2:

• Example 3:

Factoring Polynomials with a degree more than 2

• Step 1: Factor out any GCFs

• Step 2: If polynomial has 4 terms, try factoring by grouping. If not, look for sum or difference of two cubes.

• Step 3: Continue process with quadratic factors until polynomials are unfactorable.

Factoring Examples

• Example 1:

• Example 2:

• Example 3:

Factoring Examples (cont’d)

• Example 4:

• Example 5:

Homework• P. 109, #17-22, 27-30, 32-38