can someone please factor this for me?

Question

its driving me insane.

36(x^2) - 65x - 36


the x^2 is x-squared.

Answer 1

It factors to: (4x – 9) * (9x + 4)

For nasty coefficient combinations like this, I always start with the quadratic equation by considering the beast to be equal to zero and figuring the roots. Doing that gives me: x = 9/4 and x = –4/9. So then I create "factors" by doing a bit of algebra to bring the root and variable together (equal to zero) to get: (x – 9/4) = 0 and (x + 4/9) = 0.

Then I take the two "factors" and multiply each by the divisor in the non-x term (4 for the first one, 9 for the second one). Multiply the whole "factor" that is, not just the numerical term. So for the first one: (x – 9/4) * 4 = (4x – 9), and for the second one: (x + 4/9) * 9 = (9x + 4).

So now I have (4x – 9) and (9x + 4). I check this result by multiplying them and see if I have matched the original binomial. Let's see: 36x^2 + (16x – 81x) – 36 and since 16x – 81x = –65x, it matches. Done!

So to recap, you are used to seeing a quadratic equation factored to look something like: (x + 2) * (x + 3) = 0 and then setting both factors equal to zero (because one or both has to be equal to zero for that to be true) and getting, say, x = –2 and x = –3. I just reverse that, really, with the first part, and then multiply to remove the fractions. It IS a little harder to do that multiplying step if the original binomial had non-integer coefficients. Harder to DO, but just as simple in concept.

Answer 2

36(x²) - 65x - 36 =

36x² - 65x - 36 =

The middle term is - 65

Find the sum of the middle term

Multiply the first term 36 by the last term 36 equals 1296 and factor

factors of 1296 =

1 x 1296
2 x 648
3 x 432
4 x 324
6 x 216
8 x 162
9 x 144
12 x 108
16 x 81. . .<=..use these factors
18 x 72
24 + 54
27 x 48
36 x 36

- 81 and + 16 satisfy the sum of the middle term

insert - 81x and + 16x into the equation

36x² - 65x - 36

36x² - 81x + 16x - 36

Group factor

4x(9x+ 4) - 9(9x + 4)

(4x - 9)(9x + 4)

- - - - - - - - - - -s-

Answer 3

It doesn't factor into integers.

Using quadratic formula, with a = 36, b = -65 and c = -36:

x = 9/4 and -4/9

Answer 4

36(x^2 - 65/36x -1)
= 36(x^2 - 65/36 x + (65/72)^2 - (65/72)^2-1)
= 36((x-65/72)^2 - (4225 + 5184)/5184)
= 36((x-65/72)^2 - (9409/5184))
= 36((x - 65/72)^2 - (97/72)^2)
= 36 ( x - 65/72 - 97/72) ( x - 65/72 + 97/72)
= 36 ( x - 162/72)(x + 32/72)
= 36 ( x - 81/36)(x + 4/9) =
(36x - 81)( x + 4/9)

Answer 5

u can use quadratics, but u don't need it..

36x^2-65x-36

(9x+4) (4x-9)

Answer 6

-0.444, 2.25

use the quadratic formula