Question

Factor by grouping:

6k^2 + 5k - 4

So far I know that the sum = 4 and the product = 24, therefore the integers are 8 and -3

So now the equation is:
6k^2 + 8k -3k - 4

Answer 1

Factor the first two terms: 6k^2 and 8k
Factor the last two terms -3k - 4

Then notice what is common to both factorizations and factor that out as well.

Answer 2

For example:

x^2 + 5x + 6

Notice that:

3 × 2 = 6
3 + 2 = 5

Therefore:
x^2 + 5x + 6 = x^2 + 3x + 2x + 6
= x(x + 3) + 2(x + 3)
= (x + 3)(x + 2)

Answer 3

Oh alright that makes sense, I'm just having trouble making both factorizations equal:
\[6k ^{2} + 8k - 3k - 4\]
\[-3k (-k + 1) + 4 (-2k + 1)\]

Shouldn't they both be (-k + 1) or (-2k + 1)?
I think I'm just doing something wrong

Answer 4

Yes, you can only factor out what is common to both terms.

What is common to 6k^2 and 8k ? To figure that out you would need to know what is common to 6 and 8. Then what is common to k^2 and k. To figure out what is common to 6 and 8, perform an appropriate factorization of each number.

Notice that
6 = 2(3)
8 = 2(4)

k^2 = k(k)
k = k(1)

From this, you can conclude that 2k is common to 6k^2 and 8k. When you factor that out, you get

6k^2 + 8k^2 = 2k(3k + 4)

Answer 5

Alright thank you so much