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

Aug 9, 2015

$\left(6 x - 1\right) \left(3 x - 4\right)$

#### Explanation:

One technique is to employ this handy formula:

$\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

You will get;

$x = \frac{1}{6}$ and $x = \frac{4}{3}$

Rearrange them;

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

Multiply them;

$\left(6 x - 1\right) \left(3 x - 4\right)$

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.

Aug 9, 2015

Solve $y = 18 {x}^{2} - 27 x + 4$

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

#### Explanation:

Use the new AC Method. y = 18(x - p)(x - q)
Converted trinomial: $y ' = {x}^{2} - 27 x + 72 =$ (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. $p = - \frac{3}{18} = - \frac{1}{6}$ and$q = - \frac{24}{18} = - \frac{4}{3}$

$y = 18 \left(x - \frac{1}{6}\right) \left(x - \frac{4}{3}\right) = \left(6 x - 1\right) \left(3 x - 4\right)$