Factoring by gcf part 1 2nd

Factoring by gcf part 1 2nd

• 1.
  Factoring Polynomials by GreatestCommon Factor (GCF) LARRY D. BUGARING MALABON NATIONAL HIGH SCHOOL
• 2.
  Definitions To factor anexpression means to write an equivalent expression that is a product To factor a polynomial means to write the polynomial as a product of other polynomials
• 3.
  Think of theDistributive Property of Equality: a(b+c) = ab + ac  reverse it ab + ac = a(b + c) To factor the GCF out of a polynomial, we do the following: 1. Find the GCF of all the terms in the polynomial. 2. Express each term as a product of the GCF and another factor. 3. Use the distributive property to factor out the GCF.
• 4.
  Let's factor theGCF out of 2x3-6x2 1. Find the GCF of all the terms in the polynomial. 2x3 6x2 = 2 * x * x * x = 2 * 3 * x * x GCF = 2x2 2. Express each term as a product of the GCF and another factor. 2x3 6x2 = (2x2) = (2x2) (x) (3)
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  So the polynomialcan be written as 2x3 - 6x2 = (2x2) (x) - (2x2)(3) 3. Factor out the GCF Now we can apply the distributive property to factor out (2x2) (2x2) (x) - (2x2)(3) = 2x2 (x – 3) ab - ac = a(b - c)
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  Faster method Once weknow the GCF, the factored form is simply the product of that GCF and the sum or difference of the terms in the original polynomial divided by the GCF. Find the factor of 5x2 + 10x 5x2 10x = 5 * x * x = 5 *2 * x GCF = 5x 5x( 5x2 + 10x)5x 5x = 5x ( x + 2)
• 7.
  Your Turn Find thefactor form of the polynomials by GCF 1. 14x2y2z + 21xy2z2 2. 12w3t2 – 9wt2 + 15w2t3 Answer 1. 7xy2z (2x + 3z) 2. 3wt2 (4w2 – 3 + 5wt)