how you factor binomials?

Question

this is something that i learned few years ago but i forgot and i really need help with college homework thanks

Answer 1

 

It may be easier to demonstrate since you have done it before. Here are a few examples:

The sign before the constant n determines whether the factors are both positive, both negative, or opposite in sign.

 

Factor:  x² + bx + n:  Find factors of n which are both positive and add to equal b. 

Factor:  x² + bx - n:   Find factors of n. One is positive and one is negative. These add to equal b.

Factor:  x² - bx + n:   Find factors of n which are both negative and add to equal b.

Factor:  x² - bx - n:    Find factors of n. One is positive and one is negative. These add to equal b.

 

x² + 6x + 9   Factors of 9: 1,3,9   3+3=9   both factors are 3.    (x+3)(x+3) is the factored form

x² + 9x + 20  Factors of 20: 1,2,4,5,10,20   5+4=9                 (x+4)(x+5) is the factored form

x² + 1x - 6     Factors of 6:  1,2,3,6             3-2=1                  (x+3)(x-2) is the factored form

x² -2x - 8      Factors of 8:  1,2,4,8             2-4= -2                 (x+2)(x-4) is the factored form

x² + 2x - 3     Factors of 3:  1,3                   3-1=2                  (x+3)(x-1) is the factored form

x² - 10x - 24   Factors of 24:  1,2,3,4,6,8,12      12-2=10              (x+12)(x-2) is the factored form

x² + 8x  + 16  Factors of 16:  1,2,4               4+4=8                (x+4)(x+4) is the factored form

x² - 2x - 35    Factors of 35:  1,5,7               7-5=2                  (x+5)(x-2) is the factored form