Factor the trinomial 2x^2+17x+21

Answer 1

2x^2 +17x+21

a. every thing is positive so the factors will be positive

b. Factors of 2 ate (2 and 1)

d. Factors of 21 are (1 and 21) or (3 and 7) The only number we have to consider are (2,1) (1,21) and (3,7)

e. We need two combinations of these numbers that will add to give us 17 and multiply to give us 21

(2 x 7) +3 = 17 and 3 x 7 =21

So we get (2x +3) (x+7)

Answer 2

To factor 2x² + 17x + 21, we can try the "AC Method":

A = 2, C = 21, and AC = (2)(21) = 42

Find two integers with product 42 and sum 17.

3 and 14 work

2x² + 17x + 21 = 2x² + 3x + 14x + 21 = x( 2x + 3) + 7(2x + 3) = (2x + 3)(x + 7)