7.3 Part 1 Factoring Polynomials (work).notebook December 06, 2018
7.3 PART 1 FACTORING POLYNOMIALS
I. Sum and Difference of Two Cubes: a) is a binomial, b) each term is perfect cube, and c) terms are connected by addition or subtraction.
Perfect Cubes:
1 216 x3 8x6
8 343 x6 216x15
27 512 x9 64x9
64 729 x12
125 1000 x15
FACTOR PATTERNSSUM OF 2 CUBES: a3 + b3 = (a + b)(a2 ‐ ab + b2)
DIFFERENCE OF 2 CUBES: a3 ‐ b3 = (a ‐ b)(a2 + ab + b2)
Examples:1. x3 ‐ 1000 2. 8d3 + 1
7.3 Part 1 Factoring Polynomials (work).notebook December 06, 2018
Examples:3. 64y3 ‐ 1 4. 512 + 27k3
5. 216m9 + 125 6. 64 ‐ 343h3
II. GCF RevisitedREMEMBER!! The first step to factoring is LOOK FOR A GCF and factor out!7. 3d3 ‐ 81 8. 54p3 + 2
9. 6w4 + 48w 10. 16x5 ‐ 250x2
7.3 Part 1 Factoring Polynomials (work).notebook December 06, 2018
III. Factoring by Grouping11. x3 ‐ 3x2 + 5x ‐ 15 12. f3 ‐ f2 ‐ 9f + 9
13. 27q4 ‐ 27q3 + 8q ‐ 8 14. 5t4 ‐ 5t3 ‐ 20t2 + 20t
IV. Quadratic Techniques
A. Trinomials ax + bx + c (exponent of middle term is half the exponent on leading term)
n2n
15. 4x4 ‐ 17x2 + 4 16. 2h4 ‐ 9h2 + 4