Warm Up 1) 2(w + 1) 2) 3x(x 2 – 4) 2w + 23x 3 – 12x 2h Simplify. 13p Find the GCF of each pair of monomials. 3) 4h 2 and 6h 4) 13p and 26p 5.

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Warm Up 1) 2(w + 1) 2) 3x(x 2 – 4) 2w + 23x 3 – 12x 2h Simplify. 13p Find the GCF of each pair of monomials. 3) 4h 2 and 6h 4) 13p and 26p 5

Factoring by GCF Lesson 8-2

Objectives Factor polynomials by using the greatest common factor. California Standards

Factoring polynomials Answer: Answer: 4x 2 -3x = 4x 2 -3x ( )

Lets try one: 10y 3 +20y 2 -5y 2y 2 +4y-1 10y 3 +20y 2 -5y 2y 3 +4y 2 -1y Answer: 10y 3 +20y 2 -5y Answer: 10y 3 +20y 2 -5y =

You try: Factor each polynomial 1)15a-5a 2 2) -4x 2 -6x 3) -35x+424) 10g 3 -3g 5) 12h 4 +8h 2 -6h6) 3x 2 -9x+3 =5a(3-a)= -2x(2x+3) = 7(-5x+6)= g(10g 2 -3) = 2h(6h 3 +4h-3) = 3(1x 2 -3x+1)

Factoring out a common Binomial Factor Factor the expression 7(x-3) - 2x(x-3) (x-3) (x-3) Do the terms have something in common? Factor out (x-3) -2x7 (x-3) ( )

Lets try one more: Factor the expression -t(t 2 +4) + 2(t 2 +4) (t 2 +4) (t 2 +4) Do the terms have something in common? Factor out (t 2 +4) +2 -t (t 2 +4) ( )

You try: factor each expression 1)2b(b+3) + 5(b+3)2) 5(m-2) – m(m-2) 3)9x(x+4) – (x+4)4) 3x 2 (x+2) + 4(2+x) 5) 4(x-3) – x(y+2) (b+3)(2b+5) (m-2)(5-m) (x+4)(9x-1) 1 (x+2)(3x 2 +4) Can not be factored

Factoring by Grouping. 12a 3 -9a 2 +20a-15 Step 1) Group terms that have common number or variables as a factor 5(4a-3) Step 2) Factor out the GCF of each group 12a 3 -9a a-15 3a 2 (4a-3) + Step 3) Do the terms have something in common? Step 4) factor it out (4a-3) (3a 2 +5) ( ) ( )

You try: Factor by Grouping. 9x 3 +18x 2 +2x+4 Step 1) Group terms that have common number or variables as a factor 2(x+2) Step 2) Factor out the GCF of each group 9x 3 +18x 2 + 2x+4 9x 2 (x+2)+ Step 3) Do the terms have something in common? Step 4) factor it out (x+2) (9x 2 +2) ( ) ( )

Try some more: Factor by grouping 1)6x 3 +4x 2 +3x+2 2)x 3 +4x 2 +2x+8 3)10a 3 +4a 2 +5a+2 4)7r 3 -35r 2 +6r-30 5)2m 3 +4m 2 +6m+12 6)4b 3 -6b 2 +10b-15 =(2x 2 +1)(3x+1) =10a 3 +5a+4a 2 +2 =(x 2 +2)(x+4) =(2a 2 +1)(5a+2) =(7r 2 +6)(r-5) =2(m+2)(m 2 +3) =(2b 2 +5)(2b-3)

Let’s check in… Factoring by GCF Find the ________ common factor Write each term as a _______ using the GCF. Use the ______ to factor out the GCF greatest product Distributive Property

Lesson Quiz: Part I Factor each polynomial. Check your answer x + 20x m 4 – 12m 2 + 8m Factor each expression. 3. 7k(k – 3) + 4(k – 3) 4. 3y(2y + 3) – 5(2y + 3) (2y + 3)(3y – 5) (k – 3)(7k + 4) 4m(m 3 – 3m + 2) 4x(4 + 5x 2 )

Lesson Quiz: Part II Factor each polynomial by grouping. Check your answer. 5. 2x 3 + x 2 – 6x – p 4 – 2p p – A rocket is fired vertically into the air at 40 m/s. The expression –5t t + 20 gives the rocket’s height after t seconds. Factor this expression. –5(t 2 – 8t – 4) (7p – 2)(p 3 + 9) (2x + 1)(x 2 – 3)