Simple Factoring Objective: Find the greatest common factor in and factor polynomials.

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Presentation transcript:

Simple Factoring Objective: Find the greatest common factor in and factor polynomials.

Greatest common factor (GCF) The largest of the common factors of two or more numbers.

Polynomial Many terms containing a combination of variables, constants, and positive exponents that are added.

Distributive property Multiplying a single term and a polynomial.

Distributive Property Examples and Practice Examples: 2(50 + 3) = = 106 2(x + 3) = 2x + 6 y(x + 1) = yx + y y(x + y 2 ) = yx + y 3 Practice: 3(10 + 6) 3(x + 6) y(x + 6) y(x + y 4 ) To multiply common bases with exponents: Keep the base and add the exponents. x 2 (x 3 ) = x 5 y 4 (y 7 ) = y 11 z 23 (z 3 ) = z 25

Find the Greatest Common Factor Find the greatest common factor: x – 4x3y +6y 2 8d 3 + 4d d

Factoring: The distributive property in reverse: 1)Identify the GCF 2)Divide each term by the GCF 3)Place the GCF in front of parentheses 4)Place the remainder in the parentheses 5)Check: Does using the distributive property result in the original expression? 3x + bx 1)GCF = x 2)3x/x = 3 bx/x = b 3-4) x(3 + b) 5)3x + bx

Factoring Practice ax – cx 9x – 3y ax – bx 4x – 12y 25y – 35y 2 12y 2 – 36y y 4