022a65c2-ultiply-to-8-to-factor-it-is-that-suggestion-valid-choose-the-best-just

Question

You encounter the expression: $$3x2+14x+83x^2 + 14x + 8. A $$peer suggests that directly finding integers which will add to 14 and multiply to 8 will factor this expression. Is this suggestion valid? Choose the best justification.

Accepted Answer

No, because the leading coefficient is 3, you cannot directly look for integers which will add to 14 and multiply to 8; instead one must use the AC method or factor by grouping

Answer

Yes, the method works for any quadratic expression regardless of the leading coefficient, so the peer is correct

Answer

Yes, but only if you first divide the whole polynomial by 3 to make the leading coefficient equal to 1

Answer

No, because 8 is not prime, and this particular pairing strategy fails only for composite constants

You encounter the expression: 3x2+14x+83x^2 + 14x + 8. A peer suggests that directly finding integers which will add to 14 and multiply to 8 will factor this expression. Is this suggestion valid? Choose the best justification.

You encounter the expression: $3 x^{2} + 14 x + 8$ . A peer suggests that directly finding integers which will add to 14 and multiply to 8 will factor this expression. Is this suggestion valid? Choose the best justification.