Factoring polynomials using greatest common factor

powerpoint presentation

1. Factoring Polynomials Using the Greatest Common Factor

2. The Greatest Monomial Factor of two or more terms is the product of all prime algebraic factors to every term, each to the highest power that it occurs in all the terms . Check your answer by multiplying the factors.

3. Example 1 . Factor out 4x 2 + 6x 3 . Find first the GCF (Greatest Common Factor). Observe the following. 4x 2 = 2 . 2 . x . x 6x 3 = 2 . 3 . x . x . x = 2x 2 The GCF is 2x 2 . Factor out 2x 2 from the given polynomial. = 4x 2 + 6x 3 = 2x 2 ( 2 + 3x) Hence, the factored form of 4x 2 + 6x 3 is 2x 2 (2 + 3x).

4. Example 2 . Factor out a 2 + 2a – a 2 b. Find the GCF. a 2 = a. a 2a = 2 . a a 2 b = a . a . b = a The GCF is a . Factor out a from the given polynomial. = a 2 + 2a – a 2 b = a(a + 2 – ab ) Hence the factored form a 2 + 2a – a 2 b is a(a + 2 – ab ).

5. Example 3 . Factor out 5x 3 + 3x 5 . Find the GCF. 5x 3 = 5 . x . x . x 3x 5 = 3 . x . x . x . x. x = x 3 The GCF is x 3 . Factor out x 3 from the given polynomial. = 5x 3 + 3x 5 = x 3 (5 + 3x 2 ) Hence the factored form of 5x 3 + 3x 5 is x 3 (5 + 3x 2 ) .

6. Example 4 . Factor 15a 2 b – 10ab. Find the GCF. 15a 2 b = 5 . 3 . a . a. b 10ab = 5 . 2 . a . b = 5ab The GCF is 5ab . Factor out the GCF from the given polynomial. = 15a 2 b – 10ab = 5ab(3a – 2) Hence the factored form is 5ab(3a – 2).

7. Example 5 . Factor 16x 2 y + 10xy 2 – 8xy Find the GCF. 16x 2 y = 2 . 2 . 2 . 2 . x . x . y 10xy2 = 5 . 2 . x . y . y 8xy = 2 . 2 . 2 . x . Y = 2xy The GCF is 2xy . Factored out the GCF from the given factor. = 16x 2 y + 10xy 2 – 8xy = 2xy(8x + 5y – 4) Hence the factored form is 2xy(8x + 5y – 4) .