Answer:
(x - 3)(2x + 7) = 2x^2 + x - 21
Step-by-step explanation:
2x^2 + x - 21 = (__ - 3)(__ + 7)
The first term of the trinomial is 2x^2 which can be factored into 2x * 2.
You need to place 2x in one blank and x in the other blank.
Try it both ways. Then multiply the factors out to see which one gives you the correct middle term.
Try 2x - 3.
(2x - 3)(x + 7) = 2x^2 + 14x - 3x - 21 = 2x^2 + 11x - 21
This gives the middle term 11x, but we need the middle term to be x, so now we try x - 3.
(x - 3)(2x + 7) = 2x^2 + 7x - 6x - 21 = 2x^2 + x - 21
This gives the correct middle term, x, so this is the correct factorization.
Answer:
(x - 3)(2x + 7) = 2x^2 + x - 21
