Factoring Completely Your factoring tools Factoring a GCF

Factoring Completely

Your factoring tools • Factoring a GCF • Factoring the difference of two perfect squares • Factoring quadratic trinomials (A=1) • Factoring quadratic trinomials (A>1)

Factoring a GCF • Find the greatest common factor and factor it out of the polynomial • Make sure to divide everything by the GCF Examples: 1) 3 x + 6 3(x + 2) 2) x 3 - 5 x 2 + 7 x x(x 2 - 5 x + 7) 3) 15 x 5 + 25 x 3(3 x 2 + 5)

Factoring the difference of two perfect squares • Is the first term a perfect square? • Is the last term a perfect square? • Is the sign between them a minus sign? Examples: 1) x 2 - 49 (x + 7)(x - 7) 2) 25 x 2 - 81 (5 x + 9)(5 x - 9) 3) x 4 - 121 (x 2 + 11)(x 2 - 11) 4) 16 x 6 - 225 y 2 (4 x 3 + 15 y)(4 x 3 - 15 y)

Factoring quadratic trinomials (A=1) • X Method (or Guess and Check or Box Method) Examples: 1) x 2 + 10 x + 9 (x + 1)(x + 9) 2) x 2 - 11 x + 30 (x - 5)(x - 6) 3) x 2 - 16 x - 36 (x - 18)(x + 2)

Factoring quadratic trinomials (A>1) Umbrella-Method 3) 3 x 2 + 8 x + 5 4) 6 x 2 + 5 x - 4

Factoring completely (using more than one tool) 1) 2 7 x - 28 2 7(x - 4) 7(x + 2)(x - 2)

Factoring completely (using more than one tool) 2) 3 20 x - 5 x 2 5 x(4 x - 1) 5 x(2 x + 1)(2 x - 1)

Factoring completely (using more than one tool) 3) 4 x - 81 2 (x 2 9)(x + - 9) 2 (x + 9)(x + 3)(x - 3)

Factoring completely (using more than one tool) 4) 2 4 x - 16 x + 16 2 4(x - 4 x + 4) 4(x - 2)

Factoring completely (using more than one tool) 5) 3 6 x + 2 6 x(x 2 18 x - 24 x + 3 x - 4) 6 x(x + 4)(x - 1)

Factoring completely (using more than one tool) 6) 2 15 x - 2 x - 8 (3 x + 2)(5 x - 4)

Factoring completely *7) 12 x 2 + 3 x - 9 Factor the GCF first !!! 3(4 x 2 + x - 3) 3(x + 1)(4 x - 3)