Factoring #4 Warm up Answers 2x 2 (x + 3) 2) (x + 3)(x + 6) 3) (x – 10)(x + 10) 4) (y – 2)( 3x + 8) 1)2x 3 + 6x 2 2) x 2 + 9x + 18 3) x 2 -100 4) 3xy –

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Factoring #4 Warm up Answers 2x 2 (x + 3) 2) (x + 3)(x + 6) 3) (x – 10)(x + 10) 4) (y – 2)( 3x + 8) 1)2x 3 + 6x 2 2) x 2 + 9x ) x ) 3xy – 6x + 8y - 16

Factoring: Just the Factors What is a factor? The 2 terms that you would multiply together to get a third term. When will I use factoring? When given a polynomial you can find the factors to assist you in finding the x intercepts….to come in the future! What are factors in numeric expressions? The numbers you multiply together to get your original number. Ex. The number 8 has factors of 1 and 8, or 2 and 4

Factoring: Follow the steps! 1) Factor out the GCF if possible…….this is a must! Ex. 1) 4x x (x 2 + 4x + 4) 2) Write 2 sets of ( ). Put the ax term in the 1 st and 3 rd position. 4(x ___)(x ____) 3) Multiply a and c Hint: ax 2 +bx + c 1 x 4 = 4 write this number down above the b term. 4) What factors of step 3 add up to the b term? Insert the correct terms into position 2 and 4 1,4 or 2,2 4(x +2)(x+2) 5) Simplify each set of ( ) if you can.

What happens when the a coefficient is not 1? Ex 2) 3b 2 + 7b + 2 Step 1 GCF Step 2 Two sets of ( ) Done Step 3 multiply a and c Factors of 6 are: 1*6, 2*3 Step 4 Factors that add to b put in 2 nd and 4 th position. (3x + 1)(3x + 6) Step 5 Simplify if you can (3b ___)(3b ___) 3 * 2 = 6 (3x + 1)(x + 2)

Ex 3 6x 2 – 26x – 20 Nothing different! Just do the steps 2(3x 2 – 13x -10) GCF 2(3x ____)(3x ____) Two sets of ( ) ax term in 1 st and 3rd 3 x (-10) = - 30 Multiply a x c -1,30 -30,1 -2,15 -15,2 -3,10 -10,3 -5,6 -6,5 What factors add up to the b term? Place in 2 nd and 4 th position 2(3x -15)(3x + 2) Reduce 2(x-5)(3x+2)

No middle term. Who cares….I know the steps! Ex. 4) 2a (a 2 – 4) GCF 2(a ____)(a ____) 2 sets of ( ) Fill in 1 st and 3 rd position 1 x -4 = - 4 Multiply a x c 1, -4 -1,4 2, -2 What are factors that add to b term…which is zero? 2(a + 2)(a – 2)

You Try Some 1)8y y – 6 2)5x 2 + y – 6 3)3a a + 8 Answers 1) (y + 2)(8y – 3) (5x + 6)(x – 1) (a + 4)(3a + 2)