Factoring out the GCF.

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Presentation transcript:

Factoring out the GCF

What does it mean to factor a number? I can factor the number 12 in different ways… 12 = 1 x 12 12 = 2 x 6 12 = 3 x 4 12 = 2 x 2 x 3 12 = 0.5 x 24 A simple way to think of factoring is to break a “number” down into 2 or more pieces that when multiplied will give you that number back again.

Therefore, this is the first factor. Example #1: Factor. 25x2 + 60x4 – 35x3 = 5x2( 5 + 12x2 – 7x) Always when asked to factor an algebraic expression, begin by looking for a GCF Now divide 5x2 into each term of the original expression… 25x2 ÷ 5x2 = 5 60x4 ÷ 5x2 = 12x2 35x3 ÷ 5x2 = 7x The GCF(25x2, 60x4, 35x3) = 5x2 Therefore, this is the first factor.

24x5y3 – 32x2y4 = 8x2y3( 3x3 – 4y) GCF(24x5y3, 32x2y4) = 8x2y3 Example #2: Factor 24x5y3 – 32x2y4 = 8x2y3( 3x3 – 4y) GCF(24x5y3, 32x2y4) = 8x2y3

Example #3: Factor 12a4b2 – 18a5b + 30a3b3 = 6a3b( 2ab – 3a2 + 5b2) GCF(12a4b2, 18a5b, 30a3b3) = 6a3b

14x3 – 21x5 + 7x2 = 7x2( 2x – 3x3 + 1) GCF(14x3, 21x5, 7x2) = 7x2 Example #4: Factor 14x3 – 21x5 + 7x2 = 7x2( 2x – 3x3 + 1) GCF(14x3, 21x5, 7x2) = 7x2

Example #5: Factor x

Example #6: Factor 3