Download presentation

Presentation is loading. Please wait.

Published byTheresa Mencer Modified over 2 years ago

1
Follow these basic steps …

2
Factor out the GCF.

3
Count how many terms and try the following tactics. Then, go to step 3. 2 terms -- difference of 2 squares: a 2 – b 2 = (a + b)(a – b) Example:Factor 64x 4 – 9y 2 a = 8x 2 and b = 3y = (8x 2 + 3y)(8x 2 – 3y)

4
2 terms -- difference of 2 cubes: a 3 – b 3 = (a - b)(a 2 + ab + b 2 ) Example:Factor 8x 3 – y 3 SOMPS = (2x- y)( SOMPS S q u a r e f i r s t t e r m O p p o s i t e s i g n M u l t i p l y P l u s S q u a r e S e c o n d t e r m 4x 2 +2xy+y2)y2)

5
2 terms -- sum of 2 cubes: a 3 + b 3 = (a + b)(a 2 - ab + b 2 ) Example:Factor 64s 3 + t 6 SOMPS ** Notice that SOMPS still works here. = (4s+ t 2 )(16s 2 -4st 2 +t4)t4) NOTE: a 2 + b 2 is NOT factorable.

6
3 terms -- Set up 2 ( )’s use factors of 1 st term and last term until you get a pair that works with middle terms (guess and check) Example:Factor x 2 - 7x - 18 1, 1 1,18 2,9 3,6 Signs must be different = (1x + 2)(1x – 9) Check middle terms 2x -9x -7x Matches middle term of original. Yea!

7
Example:Factor 6x 2 + 17x + 12 Signs must be the same 1, 6 2,3 1,12 2,6 3,4 = (3x + 4)(2x + 3) 8x 9x 17x ** This can be exhausting (trying to pick the factors that work)! Try alternate method

8
4 or more terms -- Try grouping Intro: Factor xz – xy =x(z – y) Factor (x + 2)z – (x + 2)y = (x + 2)(z – y) Example:Factor 2x + x 2 – 6y – 3xy S1: group the terms – I pick the 1 st and the 3 rd terms; I reorder. = 2x – 6y + x 2 – 3xy S2: Factor out the GCF from each pair = 2 + x (x – 3y) S3: Since (x – 3y) is the same in both terms – factor it out. = (x – 3y)(2 + x)

9
Repeat steps until all factors are prime; i.e., they can’t be factored anymore.

10
Factor 4x 6 – 64x 2 Step 1 – Factor out GCF = 4x 2 (x 4 – 16) Step 2 – Count how many terms 2 terms – it’s the difference of 2 squares = 4x 2 (x 2 + 4)(x 2 – 4) Step 3 – Keep repeating until all factors are prime = 4x 2 (x 2 + 4)(x + 2)(x - 2)

11
this will ALWAYS work with a factorable trinomial Example:Factor 6x 2 – x - 12 ax 2 + bx + c a = 6, b = -1, c = -12 STEP 1: Write in standard form and recognize a, b, and c. STEP 2: Multiply ac. (6)(-12) = -72 STEP 3: List all factors of ac. Circle the factors that add up to b. -1,72 -2,36 -3,24 -4,18 -6,12 -8,9 1,-72 2,-36 3,-24 4,-18 6,-12 8,-9

12
this will ALWAYS work with a factorable trinomial Example:Factor 6x 2 – x - 12 a = 1, b = -1, c = -12 STEP 4: Replace bx (in original) with factors. = 6x 2 – 9x + 8x - 12 STEP 5: Group 1 st two terms and last 2 terms. = 6x 2 – 9x + 8x - 12 STEP 6: Factor. = 3x + 4 (2x – 3) = (2x – 3)(3x + 4) Back to Notes

Similar presentations

OK

Special Cases of Factoring Chapter 5.5. 1. Check to see if there is a GCF. 2. Write each term as a square. 3. Write those values that are squared as the.

Special Cases of Factoring Chapter 5.5. 1. Check to see if there is a GCF. 2. Write each term as a square. 3. Write those values that are squared as the.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on natural disaster in hindi language Ppt on index numbers youtube Ppt on hybrid solar lighting system Ppt on healthy food and healthy living Ppt on aravind eye care system Ppt on business environment nature concept and significance of colors Ppt on flora and fauna of kerala Download ppt on networking Ppt on rain water harvesting download Download ppt on teachers day in india