How do i factor 12a^3-9a^2+4a-3 completly?

Question

whpalmer4 · Answer

Look at all the coefficients.  Do you see any common factors?  You can start by factoring them out.

anonymous · Answer

no i dont

anonymous · Answer

i can do gcf of 3?

whpalmer4 · Answer

There aren't any common factors, so let's try grouping pairs of terms.

$$(12a^3 - 9a^2) + (4a - 3)$$Well, look at that, we've got a common factor in the leftmost pair$$3a^2(4a-3) + (4a - 3)$$Now if we look carefully we realize that $(4a-3)$ is a common factor to both sides of that.
$$(3a^2 + 1)(4a-3)$$

anonymous · Answer

Thanks now i got it

anonymous · Answer

wait its a common factor so you replace with +1? how did you get (3a^2+1)

whpalmer4 · Answer

$$3a^2(4a-3) + 1(4a-3)$$Now do you see it?

anonymous · Answer

no i dont sorry

whpalmer4 · Answer

$$(a+b)(c+d) = a(c+d) + b(c+d)$$

whpalmer4 · Answer

We're just doing the distributive property backwards

anonymous · Answer

oh i see

anonymous · Answer

isnt it combine like terms which is why it got canceled out?

whpalmer4 · Answer

You wouldn't have any trouble if it was$$3a^2x+x$$I bet.  You'd instantly say $$x(3a^2+1)$$You just aren't used to thinking of factoring out binomials like $(4a-3)$.

whpalmer4 · Answer

But if we say $x = (4a-3)$ that's exactly what we've got!

anonymous · Answer

your correct

whpalmer4 · Answer

I know this isn't the English forum, but your answer should be "you're correct" :-)

anonymous · Answer

true lol

anonymous · Answer

im a web developer should i make english version of this site?