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

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Presentation transcript:

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

Factoring Polynomials 4.4 Factoring Polynomials Algebra II

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, 225... Learn your perfect cubes: 1, 8, 27, 64, 125, 216, 343, 512... Algebra II

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

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

Examples: Factor each binomial 5. 125 + 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

Examples: Factor each binomial 9. 25x4 – 36 **Not a Perfect Cube** (5x2 – 6)(5x2+ 6) 10. 8x3 + 27 (2x +3)(4x2 – 6x+9) 11. 125x9 – 27y3 (5x3–3y)(25x6+15x3y+9y2) 12. 9x8 – 25y6 **Not a Perfect Cube** (3x4 – 5y3)(3x4 + 5y3) Algebra II

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

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

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

Factor by Grouping: 4 Terms Only 5. x2y2 – 3x2 – 4y2 + 12 (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

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

Factor each. 1. 16x4 – 81 2. 2x6 – 6x4 – 20x2 3. 8x3 – 343 4. x4 – 6x2 – 27 5. 3x3 – 7x2 –12x + 28 6. 3x4 – x2 – 4 Algebra II

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

Student Journal Pg. 94-95: 4x3 – 4x2 + x 12x2 – 22x – 20 5m4 – 70m3 + 245m2 12x2 – 22x – 20 3m2 – 48m6 Algebra II

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