Factor the Trinomial

Question

Factor using the ax²+bx+c

2x²-3x-2

Answer 1

2x^2 -3x -2

= (2x+1)(x-2)

Answer 2

I. Start with two parenthesis:

( ) ( )

II. 2x² has only two possible factors: 2x and x. They belong to the first terms in the parenthesis

(2x ) (x )

III. -2 only has only two possible factors: (-2 and 1) or (2 and -1)

However we don't know how (-2 and 1) or (2 and -1) would be paired with 2x and x

(2x+1)(x-2) or (2x-1)(x+2) or (2x-2)(x+1) or (2x+2)(x-1)

IV. Trial and error with FOIL

(2x+1)(x-2)= 2x²-4x+1x-2 = 2x²-3x-2

(2x-1)(x+2)= 2x² +4x-x-2= 2x² +3x-2

(2x-2)(x+1)= 2x²+2x-2x-2= 2x² -2

(2x+2)(x-1) = 2x²-2x+2x-2= 2x² -2

Which one of the factors are you looking for?

(2x+1)(x-2)= 2x²-4x+1x-2 = 2x²-3x-2