Factoring with GCF and DOS

Table of Contents 46: Warm-Up, Guided Practice, Reflection 47: How Do I Factor Quadratics Using Greatest Common Factor (GCF) and Difference of Squares (DOS)?

Warm-Up List all the square from 1 to 20 # Sq 1 8 15 2 9 16 3 10 17 4 11 18 5 12 19 6 13 20 7 14 1 64 225 4 81 256 9 100 289 16 121 324 25 144 361 36 169 400 49 196

Padlet Warm Up List what you know about the graphs/equations of: F(x) = A(x – r)(x – s) G(x) = Ax2 + Bx + C Period 4 Period 6

Learning Intention/Success Criteria LI: We are learning to factor quadratics using difference of squares (DOS) and greatest common factor (GCF) SC: I know how to -recognize if a quadratic can be factored -identify the roots and y-intercept of a quadratic -identify the solutions of the equation by factoring -square and square root numbers -find the GCF -check my work by multiplying binomials

EQ: How Do I Factor Using Difference of Squares and Greatest Common Factor? 5/19/2019

Teach Me How To Factor Video

Greatest Common Factor (GCF) The largest term that divides evenly into a given polynomial Perfect Square Any number that is a square of a rational number Prime A positive integer or term which has only the number 1 and itself as factors

Difference of Squares Two perfect squares separated by a subtraction sign a2 – b2 = (a + b)(a – b)

Example 1: Factor the polynomial using GCF 10x2 + 5x First Term: Second Term: 5 • 2 • x • x 5 • 1 • x 5x (2x + 1)

Factor the polynomial using GCF: 7x – 21 Guided Practice 1 Factor the polynomial using GCF: 7x – 21 A] Prime B] 7(x – 3) C] 7(x – 21) D] 3(7x – 7)

Factor the polynomial using GCF: 16x3 + 24x2 – 8x Guided Practice 2 Factor the polynomial using GCF: 16x3 + 24x2 – 8x A] 4(4x3 + 6x2 – 2x) B] 4x(4x2 + 6x – 2) C] 8x(2x2 + 3x – 1) D] 2x(8x2 + 12x – 4)

Factor the polynomial using GCF: 7x3 – 5z2 + 3x2z2 Guided Practice 3 Factor the polynomial using GCF: 7x3 – 5z2 + 3x2z2 A] x2z2(7x – 5 + 3) B] 5z2(7x3 – 1 + 3x2) C] 7x2(x – 5z2 + 3z2) D] Prime

Predict What is the difference between the words “factor” and “solve”?

Example 2a: Factor x2 – 81 x2 – 81 First Term Coefficient: First Term Variable: Second Term: 1 = 1 x2 = x 81 = 9 (x + 9)(x – 9)

Example 2b: Find the roots (x + 9)(x – 9) = 0 x + 9 = 0 x – 9 = 0 -9 + 9 _________ -9 + 9 _________ x = - 9 x = 9

Factor the polynomial: x2 – 144 Guided Practice 4a Factor the polynomial: x2 – 144 A] (x + 12)(x – 12) B] (x + 72)(x – 72) C] (x + 36)(x – 36) D] Prime

Find the roots: (x + 12)(x – 12) = 0 Guided Practice 4b Find the roots: (x + 12)(x – 12) = 0 A] x = 12 and -12 B] x = 12 C] x = -12 D] Prime

Factor the polynomial : x2 – 49 Guided Practice 5a Factor the polynomial : x2 – 49 A] (x + 49)(x – 49) B] (x + 24.5)(x – 24.5) C] (x + 7)(x – 7) D] Prime

Find the roots: (x + 7)(x – 7) = 0 Guided Practice 5b Find the roots: (x + 7)(x – 7) = 0 A] x = 7 B] x = -7 C] x = 7 and -7 D] Prime

Factor the polynomial: x2 + 121 Guided Practice 6 Factor the polynomial: x2 + 121 A] (x + 121)(x – 121) B] (x + 60.5)(x – 60.5) C] (x + 11)(x – 11) D] Prime

Predict Do you think you can use GCF and Difference of Squares at the same time? Why or why not?

Example 3: Factor 2x2 - 72 2x2 – 72 First Term: Second Term: 2 • 1 • x • x 2 • 36 2(x2 – 36) = 1 First Term Coefficient: First Term Variable: Second Term: 1 x2 = x 36 = 6 2(x + 6)(x – 6)

Factor the polynomial: 4x2 – 121 Guided Practice 7 Factor the polynomial: 4x2 – 121 A] (2x + 11)(2x – 11) B] 4(x2 – 30.25) C] (2x + 60.5)(2x – 60.5) D] Prime

Find the roots: (2x + 11)(2x – 11) = 0 Guided Practice 7 Find the roots: (2x + 11)(2x – 11) = 0 A] x = 5.5 B] x = -5.5 C] x = 5.5 and -5.5 D] Prime

Factor the polynomial: 3x2 – 507 Guided Practice 8a Factor the polynomial: 3x2 – 507 A] 3(x2 + 169) B] 3(x + 13)(x – 13) C] 3(x2 – 169) D] Prime

Find the roots: 3(x + 13)(x – 13) = 0 Guided Practice 8a Find the roots: 3(x + 13)(x – 13) = 0 A] x = 169 B] x = 13 and -13 C] x = 13 D] Prime

Factor the polynomial: 4x2 + 25 Guided Practice 9 Factor the polynomial: 4x2 + 25 A] 4(x2 + 6.25) B] (2x + 5)(2x – 5) C] 2(2x + 12.5)(2x – 12.5) D] Prime

Predict Once a polynomial is factored and solved, what does your answer show you?