Factoring with DOS.

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Presentation transcript:

Factoring with DOS

Learning Intention/Success Criteria LI: We are learning to factor quadratics using difference of squares (DOS) 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

Example 1a: 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 First Term Coefficient: First Term Variable: Second Term:

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 First Term Coefficient: First Term Variable: Second Term:

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

Example 2: 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 GCF: First Term Coefficient: First Term Variable: Second Term: 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 GCF: First Term Coefficient: First Term Variable: Second Term: 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