How would you factor 8x^2-6x-5?

Question

thank you to everyone who answered my last factoring question, but what do you do if theres a number in front of the x^2?

Answer 1

If there is a number in front of the x, you have to find two numbers that equal that number when multiplied together and that, when added together, equal your B number (-6 in this example). So, if you multiply -4 and -2, you get positive 8, which fits in with what we have. If you add -4 and -2, you get -6, which fits in. So far we have

(-2x + ) (-4x + )

Now we need to fill in the last number on both sides. What two numbers, when multiplied, will equal -5? -1 and 5 will work.
(-2x + -1)(-4x + 5)
Now we can FOIL to check our answer (Multiply First, Inner, Outer, and Last in each side).

First:-2x * -4x = -8x^2
Outer: -2x * 5 = -10x
Inner: -1*-4x = 4x.
Last: -1 * 5 = -5.
So we have:
-8x^2 - 10x + 4x - 5.

The -10x and 4x are like terms, so when we add them together, we yield (-10x + 4x = -6x).

We're left with:
-8x^2 - 6x - 5 after we check by FOILing. We've done it correctly.

Answer 2

First: multiply the 1st & 3rd term (-5*8 = -40). find two numbers that give you (- 40) when multiplied & -6 (2nd term) when added/subtracted. the numbers are (-10 & 4).

SeC: rewrite the expression with the new middle terms.

8x^2 - 10x + 4x - 5

Third: 4 terms - group "like" terms & factor both sets of parenthesis.

(8x^2 + 4x) - (10x - 5)
4x(2x+1) - 5(2x + 1)

*Inner terms have to match - combine the inner terms (once) with the outer terms.

(2x+1)(4x-5), or (4x-5)(2x+1)

Answer 3

you could use the quadratic formula, or

what multiplies to 8? --> 1 & 8 or 2 & 4
so you're gonna have (1x ....) (8x....) or (2x....)(4x.....)

and then you also need to look at what multiplies to 5 --> the only choice is 1 & 5
Also, since the 6x & the 5 are both negative you will have one + and one - in the ( )
trial and error
(1x-1)(8x+5) or (1x+1)(8x-5) or (1x-5)(8x+1) or (1x+5)(8x-1)
(2x-1)(4x+5) or (2x+1)(4x-5) or (2x+5)(4x-1) or (2x-5)(4x+1)

the right answer is (4x-5)(2x+1)


you kinda have to try the combinations to see what would work, after you've done enuf factoring it will get easier to see what numbers to choose.

Answer 4

(4x - 5) (2x + 1)

I use trial and error.
You could use the quadradic equation.

Hopefully ,this is correct