Factoring Completely.

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Presentation transcript:

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) 3x + 6 3(x + 2) 2) x3 - 5x2 + 7x x(x2 - 5x + 7) 3) 15x5 + 25x3 5x3(3x2 + 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) x2 - 49 (x + 7)(x - 7) 2) 25x2 - 81 (5x + 9)(5x - 9) 3) x4 - 121 (x2 + 11)(x2 - 11) 4) 16x6 - 225y2 (4x3 + 15y)(4x3 - 15y)

Factoring quadratic trinomials (A=1) X Method (or Guess and Check or Box Method) Examples: 1) x2 + 10x + 9 (x + 1)(x + 9) 2) x2 - 11x + 30 (x - 5)(x - 6) 3) x2 - 16x - 36 (x - 18)(x + 2)

Factoring quadratic trinomials (A>1) Umbrella-Method 3) 3x2 + 8x + 5 4) 6x2 + 5x - 4

Factoring completely (using more than one tool) 1) 7x2 - 28 7(x2 - 4) 7(x + 2)(x - 2)

Factoring completely (using more than one tool) 2) 20x3 - 5x 5x(4x2 - 1) 5x(2x + 1)(2x - 1)

Factoring completely (using more than one tool) 3) x4 - 81 (x2 + 9)(x2 - 9) (x2 + 9)(x + 3)(x - 3)

Factoring completely (using more than one tool) 4) 4x2 - 16x + 16 4(x2 - 4x + 4) 4(x - 2)(x - 2)

Factoring completely (using more than one tool) 5) 6x3 + 18x2 - 24x 6x(x2 + 3x - 4) 6x(x + 4)(x - 1)

Factoring completely (using more than one tool) 6) 15x2 - 2x - 8 (3x + 2)(5x - 4)

Factoring completely *7) 12x2 + 3x - 9 Factor the GCF first !!!