Review Factoring of Algebra

University:
High School
Course:
High School Algebra
Academic year:

2022
Views:

14

Pages:

2
Author:

stickigyq

Yes…Factoring! In Chapter 2, you will need to remember how to do this. Below are the steps to follow (in order). 1) Look for common #s. What is the biggest number that you can divide out from all the terms? Example: 3a + 12 3(a + 4) 2) Look for common variable. What variables do all the terms share? Example: 3a2 + a3b a2(3 + ab) 3) Does the polynomial fit any of these special descriptions? Difference of Squares Trinomial Squares Grouping --Two Terms --Three Terms --Four Terms --Both perfect Squares --Two perfect Squares --A Difference (--) Sign --Middle = 2AB A2 – B2 A2 + 2AB + B2 (A + B)(A – B) x3 – 3x2 + 2x – 6 x2(x – 3) + 2(x – 3) (A + B)(A + B) or A2 – 2AB + B2 (x2 + 2)(x – 3) (A – B)(A – B) 4) Factor or un-Distribute your polynomial/trinomial. a) No # in the front? x2 + bx + c --Use a combination [two numbers] that b) # in the front --Move # “a” to the back by multiplying multiply to “c” …..but add up to “b” --Then factor as x2 + 12x + 20 Example: Example: 1 • 20 2 • 10 4•5 ax2 + bx + c 2x2 + 11x + 12 x2 + 11x + 24 . 1 • 24 2 • 12 3•8 4•6 (x2 + 2)(x + 10) (x2 + 3 )(x + 8 ) --move # “a” back 2 2 (2x2 + 3)(x + 4) Factor. (you may be asked to perform two of the steps on one problem) If not factorable, write simplified 1) 18x6 – 21x9 2) 3x2 + 12x + x + 4 3) 2x3 – 6x2 + 6x 4) 9x2 – 12x + 4 5) 5x3 – 5x2 – 30x 6) x2 – 169 7) 30x2 + 11x + 1 8) 5x2 – 18x + 16 9) 20x2 + 2x – 6 10) 3x4 – 15x3 + 2x – 10 11) 6x2 – 7x – 5 12) 12x2 – 75 13) x2 + 7x – 8 14) 2x3 + 4x2 + 6x 15) 25x2 + 20x + 4 16) 6x2 – 7x + 2 17) 36x2 – 64 18) x2 – 16x + 36