Question

Factoring 6x²+5x-6

Answer 1

@Marleny69, Do you have a specific question concerning this problem?

Answer 2

yes how factor by grouping this problem

Answer 3

Find two numbers \(m\) and \(n\) so that

\(m \times n = -36\)
\(m + n = 5\)

Answer 4

That's the first step in factor by grouping. @Marleny69, can you figure out the two numbers?

Answer 5

I got -36, but how i get 5 from m+n

Answer 6

You have to find two numbers that multiply to get -36. Those same two numbers need to add to get 5

Answer 7

Think of all pairs of integers that multiply to get -36.

Answer 8

Obviously \(6 \times 6 = 36\) but \(6 + 6 = 12 \ne 5\)

Answer 9

9x4=36 also they are the two number?

Answer 10

(9)(-4) = -36
9 - 4 = 5

Answer 11

So the two numbers are 9 and -4

Answer 12

The next step is to replace 5 with 9 - 4

Answer 13

\(6x^2 + (9 - 4)x - 6\)

Answer 14

Then distribute x:

\(6x^2 + 9x - 4x - 6\)

Answer 15

Next factor the first two terms:
\(6x^2 + 9x\)

Then factor the last two terms:
\(-4x - 6\)

After factoring both sets of terms, you should notice a factor common to both factorizations

Answer 16

I see 2x+3 and 2x+3 right!

Answer 17

Okay, now according to distributive property, if you observe two terms with common factors, you're supposed to factor it out:

\(6x^2 + 9x - 4x - 6 = 3x(2x + 3) - 2(2x + 3) \)
\( = (2x + 3)(3x - 2)\)

Answer 18

ok i got you. thank you.

Answer 19

yw