Factor the following. 1) 20x 2 - 115x – 302) x 2 + 4x – 96 3)14a 2 b - 63a 5 b 6 4)12x 3 +3x 2 +20x +5.

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Presentation transcript:

Factor the following. 1) 20x x – 302) x 2 + 4x – 96 3)14a 2 b - 63a 5 b 6 4)12x 3 +3x 2 +20x +5

September 4 th

Multiply (x – 2) (x + 2)…. This product is a little different than the rest. What is it missing? A middle term!

If given x 2 – 4, and asked to factor, how could you set this up using what you know already? What is the middle coefficient, b ? What is the last number, c ? Can you find two numbers that add to be zero and multiply to be – 4 ? -4 0

a 2 - b 2 = (a - b) (a + b) x = (x - 2) (x + 2) x 2 – 4 = (x - 2) (x + 2) This only works for the DIFFERENCE, not sum/addition!

Factor x = (a - b) (a + b) What number squared is 9? So… (x - 3) (x + 3) Check your answer by FOIL or box!

What if there is a coefficient in the front? 4x 2 – 25 It works the same way! What number squared is 4? 25? (2x - 5) (2x + 5)

1) x 2 – 144 2) w 2 – 64 3) 16m 2 – 49 4) x

Multiply (x + 6) (x + 6)…. What do you notice about the product? Can you find a pattern?

a 2 + 2ab + b 2 = (a + b) (a + b) x 2 + 8x + 16 = (x + 4) (x + 4) x 2 +2(1)(4) = (x + 4) (x + 4) If you are having trouble recognizing the pattern, practice factoring like we did earlier.

1) x 2 + 6x + 9 2) x x + 25

a 2 - 2ab + b 2 = (a - b) (a - b) x x + 49= (x - 7) (x - 7) x 2 – 2(1)(7) = (x - 7) (x - 7) Why do we ADD b 2 ?

1) x x ) x x + 100

What if there is a coefficient in the front? 4x 2 – 12x + 9 What number squared is 4? 9? (2x - 3) Why is there a 12x in the middle? Check your answer!

1) 4x x ) 25z z + 16

1) 9n 2 – 42n ) 36d 2 – 60d + 25

Is 24g 2 -6 a difference of two squares? What should I do first? GCF = So…. 24g 2 – 6 = 6 (4g 2 – 1) = 6 (2g - 1) (2g + 1) Now factor using difference of squares!

1)27x x ) 8z z + 128

Find the side length of the square! Area = 25r r + 9

1. 18p 2 – m 3 – 98m

a 3 + b 3 = (a + b)(a 2 – ab + b 2 ) 27x = (3x) 3 + (1) 3 = (3x + 1)((3x) 2 – (3x)(1) ) = (3x + 1)(9x 2 – 3x + 1)

Example 1: 8k Example 2: 343u

a 3 – b 3 = (a – b)(a 2 + ab + b 2 ) x 3 – 8 = (x) 3 - (2) 3 = (x – 2) (x 2 + (2)(x) ) = (x – 2) (x 2 + 2x + 4)

Example 1: 64x 3 – 27 Example 2: 125p

a 3 ± b 3 = (a [same sign] b)(a 2 [opposite sign] ab [always positive] b 2 )

Factor: c 10 – 30c 5 d + 225d 2

If 49x 2 – kx + 36 is a perfect square trinomial, what is the value of k?

Worksheet Start thinking about your test...it’s on TUESDAY!!!