1. Bellwork: Factor Each. 5x2 + 22x + 8 4x2 – 25 81x2 – 36 20x2 – 7x – 6
Algebra II

2. Factoring Polynomials
4.4
Factoring Polynomials
Algebra II

3. Things to Know Always check for GCF first! Learn your perfect squares:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196,
Learn your perfect cubes:
1, 8, 27, 64, 125, 216, 343,
Algebra II

4. Sum or Difference of Two Cubes
(a3 + b3) = (a + b)(a2 – ab + b2)
(a3 – b3) = (a – b)(a2 + ab + b2)
S O A P
same,
opposite
Always plus
Algebra II

5. Examples: Factor each binomial
1. x3 + 8 (x + 2)(x2– 2x + 4) 2. 8x3 – 1 (2x – 1)(4x2+2x+1)
3. x3 – 27
(x – 3)(x2 + 3x + 9)
4. 8x3 – 125y6
(2x–5y2)(4x2+10xy2+25y4)
Algebra II

6. Examples: Factor each binomial
x3 (5 + x)(25 – 5x + x2) 6. 16x5 – 250x2 2x2(8x3 – 125) 2x2(2x–5)(4x2+10x+25)
7. 81x4 – 16 **Not a perfect cube** (9x2 – 4)(9x2 + 4) (3x–2)(3x+2)(9x2+4) 8. 64a4 – 27a a(64a3 – 27) a(4a–3)(16a2+12a+9)
Algebra II

7. Examples: Factor each binomial
9. 25x4 – 36 **Not a Perfect Cube** (5x2 – 6)(5x2+ 6) 10. 8x (2x +3)(4x2 – 6x+9)
x9 – 27y3 (5x3–3y)(25x6+15x3y+9y2) 12. 9x8 – 25y6 **Not a Perfect Cube** (3x4 – 5y3)(3x4 + 5y3)
Algebra II

8. Factoring 4 terms by Grouping
Group the first two and last two terms
Factor the GCF of each group
if no GCF, reorder terms and start over
Factor out the binomial that is now the GCF
Algebra II

9. Factor by Grouping: 4 Terms Only
1. x3 – 2x2 – 9x + 18 (x3 – 2x2) + (–9x + 18) x2(x – 2) – 9(x – 2) (x – 2)(x2 – 9) (x – 2)(x – 3)(x + 3)
2. bx2 + 2a + 2b + ax2 (bx2 + 2a) + (2b + ax2) No GCF, so reorder. (bx2+2b) + (2a + ax2) b(x2 + 2) + a(2 + x2) (x2 + 2)(b + a)
Algebra II

10. Factor by Grouping: 4 Terms Only
3. 8x3 – 12x2 – 2x + 3 (8x3 – 12x2) + (–2x + 3) 4x2(2x – 3) –1(2x – 3) (2x – 3)(4x2 – 1) (2x – 3)(2x – 1)(2x + 1)
4. 2x3 – x2 + 2x – 1 (2x3 – x2) + (2x – 1) x2(2x – 1) + 1(2x–1) (2x – 1)(x2 + 1)
Algebra II

11. Factor by Grouping: 4 Terms Only
5. x2y2 – 3x2 – 4y (x2y2 – 3x2) + (– 4y2+12) x2(y2 – 3) – 4(y2 – 3) (y2 – 3)(x2 – 4) (y2 – 3)(x – 2)(x + 2)
6. 32x5 – 8x3 + 4x2 – 1 (32x5 – 8x3) + (4x2 – 1) 8x3(4x2 – 1) + 1(4x2 – 1) (4x2 – 1)(8x3 + 1) (2x–1)(2x+1)(2x+1)(4x2–2x+1)
Algebra II

12. Factoring Polynomials: 3 Terms
7. x4 – 8x2 – 9 (x2 – 9)(x2 + 1) (x – 3)(x + 3)(x2 + 1) 8. 3x4 – 8x2 + 4 (3x2 – 2)(x2 - 2)
9. 5x4 – 2x2 – 3 (5x2 + 3)(x2 – 1) (5x2 + 3)(x – 1)(x + 1) 10. 8x4 + 3x2 – 5 (8x2 – 5)(x2 + 1)
Algebra II

13. Factor each.
1. 16x4 – x6 – 6x4 – 20x2 3. 8x3 – 343
4. x4 – 6x2 – x3 – 7x2 –12x x4 – x2 – 4
Algebra II

14. Student Journal Pg. 94-95: 20x3 – 220x2 + 600x m5 – 81m 27a3 + 8b3
5t6 + 2t5 – 5t4 – 2t3
y4 – 13y2 - 48
5p3 + 5p – 5p2 – 5
810k4 – 160
a5 + a3 – a2 – 1
2x6 – 8x5 – 42x4
5z3 + 5z2 – 6z – 6
Algebra II

15. Student Journal Pg. 94-95: 4x3 – 4x2 + x 12x2 – 22x – 20
5m4 – 70m m2
12x2 – 22x – 20
3m2 – 48m6
Algebra II

16. Show that the binomial is a factor of the polynomial
Show that the binomial is a factor of the polynomial. Then factor the funtion completely.
15. f(x) = x3 – 13x – 12; x + 1
16. f(x) = 6x3 + 8x2 – 34x – 12; x – 2
17. f(x) = 2x4 – 12x3 + 6x2 + 20x; x – 5
Algebra II