FACTORING REVIEW Math 0099 Chapter 6 Created and Presented by Laura Ralston

STEP 1 STEP 1 Always check to see if you have a Greatest Common Factor (GCF). If so, remove it from the problem first. Always check to see if you have a Greatest Common Factor (GCF). If so, remove it from the problem first. b The GCF is a number, letter, or combination thereof in each term of the problem. b If the leading coefficient is negative, factor out a -1

STEP 2 Depends on the number of terms the polynomial contains Depends on the number of terms the polynomial contains A) If the polynomial has 2 terms, check to see if it is a difference of two squares by asking yourself three questions.

THE QUESTIONS b Is the first term squared? b Is the second term squared? b Is there a minus sign between terms? b You must answer YES to all three to proceed.

Difference of Two Squares a 2 - b 2 = (a + b) (a - b)

STEP 2, Part B) b If you have 4 terms, you will use grouping technique. b Break the problem into 2 smaller problems by considering the first two terms as one and the second two terms as another. b Look for GCF in each pair. Once you have removed the GCF from each pair, the expression in the parentheses should be the same. It is now the GCF.

STEP 2, Part C) b If you have 3 terms, rewrite the polynomial with 4 terms and use the grouping technique (ac method) or trial and error technique b For ac method: Multiply the coefficient on the squared term and the constant.Multiply the coefficient on the squared term and the constant. List the pairs of numbers that will give you that productList the pairs of numbers that will give you that product

Continued….. Using the sign in front of the constant, decide which pair will give you the coefficient on the middle term.Using the sign in front of the constant, decide which pair will give you the coefficient on the middle term. Rewrite and use grouping technique by replacing the middle term with the pair you selected.Rewrite and use grouping technique by replacing the middle term with the pair you selected.

STEP 3 b As a final check, see if any of the factors you have written can be factored further. If you have overlooked a common factor, you can catch it here. b Rule of thumb: exponents on variable will most often be 1.

STEP 4 b If nothing will factor, the polynomial is PRIME. b Move on to the next problem

Examples b 1) a 2 – 4a + 3 b 2) y 2 + 8y + 15

Examples b 3) x 2 + 3x - 10 b 4) m 2 – m - 6

Examples b 5) y b 6) 49x 2 + 4

Examples b 7) -2y y - 70 b 8) 3n n n

Examples b 9) x – 15x 2 b 10) 252x – 175x 3

Examples b 11) 2xz + 10x + z + 5 b 12) 2x 3 – 14x 2 – 3x + 21

Assignment Page 479 #1-65 odd