Factor the trinomial: 3x2 - 7x - 6

Question

jim_thompson5910 · Answer

Multiply the first and last coefficients: 3*(-6) = -18

Now find two numbers that both multiply to -18 and add to -7

jim_thompson5910 · Answer

Which two numbers do this?

anonymous · Answer

1 & 6 ?

jim_thompson5910 · Answer

no, 1 and 6 multiply to 6 and add to 7


The two numbers are really -9 and 2


This is because -9*2 = -18 and -9+2 = -7

jim_thompson5910 · Answer

Now that we know that the two numbers are -9 and 2, we can break up -7x into -9x+2x


So 3x^2 - 7x - 6 becomes 3x^2 - 9x + 2x - 6


Now factor by grouping


3x^2 - 9x + 2x - 6


(3x^2 - 9x) + (2x - 6)


3x(x-3) + 2(x-3)


(3x+2)(x-3)


This tells us that 3x^2 - 7x - 6 completely factors to (3x+2)(x-3)

anonymous · Answer

Thank you so much for your help, & explaining it out to me in a way I understand better.

jim_thompson5910 · Answer

you're welcome