factor the polynomial

Question

2x^2-x-6

Answer 1

You want to find a combination of factors that multiply to -6. Also, 2 times one of the number plus the other number must equal -1. First determine all factors of -6:

-1 * 6 = -6

1 * -6 = -6

-2 * 3 = 6

3 * -2 = -6

-3 * 2 = -6

3 * -2 = -6

-6 * 1 = -6

6 * -1 = -6

 

Now see which combinations fulfill the requirement for 2 times one of the number plus the other number to equal -1:

2(-1) + 6 = 4
2(1) + -6 = -4
2(-2) + 3 = -1
2(2) + -3 = 1
2(-3) + 2 = -4
2(3) + -2 = 4
2(-6) + 1 = -11
2(6) + -1 = 11

 

The only combination that satisfies both requirements would be -2 and 3. Use this pair to factor out the equation:

0 = 2x² - x - 6 = (2x + 3) (x - 2)

 

This means that either (2x+3)=0 or (x-2)=0

-->  2x + 3 = 0  -->  x = -3/2

OR

-->  x - 2 = 0  -->  x = 2

Answer 2

2x^2-x-6 is a term and cannot be factored.

 

2x² - x - 6 is a trinomial and can be factored using FOIL.

 

(2x +3)(x - 2)