Question

How do you factor `18x^2-27x+4`?

Answer 1

`(6x-1)(3x-4)`

Explanation:

One technique is to employ this handy formula:

`(-b+-sqrt(b^2-4ac))/(2a)`

You will get;

`x=1/6` and `x=4/3`

Rearrange them;

`6x-1=0` and `3x-4=0`

Multiply them;

`(6x-1)(3x-4)`

Voila!

I recommend this technique for large coefficients of `x^2`. In this case, it is 18. Because you have different possible ways to factor 18:

1 and 18, 2 and 9, 6 and 3.

This will save you the time from trial and error especially for even bigger coefficients.

Answer 2

Solve `y = 18x^2 - 27x + 4`

Ans: (6x - 1)(3x - 4)

Explanation:

Use the new AC Method. y = 18(x - p)(x - q)
Converted trinomial: `y' = x^2 - 27x + 72 =` (x - p')(x - q').
p' and q' have same sign.
Factor pairs of (72) --> (2, 36)(3, 24) . This sum is 27 = -b.
Change the sum to b. Then, p' = -3 and q' = -24.
Therefor. `p = -3/18 = -1/6` and`q = -24/18 = -4/3`

`y = 18(x - 1/6)(x - 4/3) = (6x - 1)(3x - 4)`