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.
Many terms containing a combination of variables, constants, and positive exponents that are added.
Multiplying a single term and a polynomial.
Distributive Property Examples and Practice 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 26 Examples: 2(50 + 3) = 100 + 6 = 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 )
Find the Greatest Common Factor Find the greatest common factor: 10 + 5 2x – 4x 3y +6y 2 8d 3 + 4d 2 + 12d
Factoring: The distributive property in reverse:
Identify the GCF
Divide each term by the GCF
Place the GCF in front of parentheses
Place the remainder in the parentheses
Check: Does using the distributive property result in the original expression?