How do you factor 4x^3-13x^2+3x?

I started by taking the GCF (x) out, and I got 4x^2-13x+3, but after that, I'm not sure what to do.

Question

How do you factor 4x^3-13x^2+3x?

I started by taking the GCF (x) out, and I got 4x^2-13x+3, but after that, I'm not sure what to do.

hero · Answer

If you factored out x then you have

$$x(4x^2 - 13x + 3)$$

Now find two numbers, $m$ and $n$ that add to get -13, yet multiply to get 12.

$$m + n = -13 \ m \times n = 12$$

anonymous · Answer

-12 and -1

I tried that, but then when I put them in factored for, I tried checking for the answer and it didn't work.

(4x-1) (4x-12)

hero · Answer

Okay, I see that your factorization is not correct.

hero · Answer

Here's what you're supposed to do after finding the two numbers

$x(4x^2 -13x + 3)=x(4x^2 -12x - 1x + 3)$
                           $=x(4x(x - 3) -1(x - 3))$
                           $=x((x - 3)(4x - 1))$
                           $=x(x - 3)(4x - 1)$

anonymous · Answer

THANK YOU! I wasn't taught that method, but now that you've shown me, THANKS! 

If this were any other problem where I didn't have a GCF, could I still keep the -12x and -1x separate?

hero · Answer

Yes. The method is called factor by grouping. If the quadratic is factorable, then you can use that method. However, you have to know what you're doing in order to use it.

anonymous · Answer

Yup, I understand, thank you!

anonymous · Answer

Quick question, sorry to come back to this problem again, but the -1x+3... when you factored the -1 out, are you allowed to change the sign from a + to a - inside the parentheses of the x+3?

hero · Answer

Basically....

Suppose you had

$$-1(x - 3)$$

And you were asked to use the distributive property to expand the expression...what would be the result?

hero · Answer

If you were to expand the expression using the distributive property, you would see that you arrive back at the original expression which is $-1x + 3$ because
$-1(x - 3) = -1(x) -1(-3)= -1x + 3$