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