Help with factorising

**briggott** · June 10th 2009, 10:26 AM

I am need of help please!

We have just started doing factorising in math and I am stumped by the following:

21a^2y^3q-14y^4q^3+7y^2q
I need to factorise this, I understand that I have to take out the common factors but don't know where to start!
Thanks in advance!

**alexmahone** · June 10th 2009, 10:32 AM

$21a^2y^3q-14y^4q^3+7y^2q$
= $7(3a^2y^3q-2y^4q^3+y^2q)$
= $7y^2q(3a^2y-2y^2q^2+1)$

**VonNemo19** · June 10th 2009, 01:35 PM

Originally Posted by briggott

I am need of help please!

We have just started doing factorising in math and I am stumped by the following:

21a^2y^3q-14y^4q^3+7y^2q
I need to factorise this, I understand that I have to take out the common factors but don't know where to start!
Thanks in advance!

Listen man, I just wanted to give you a quick breakdown. When factorin a polynomial, all you have to do is figure out what all the terms have in common, and then take out the biggest one you can. Look at this:

$ab^2c^4x^7yz^9+a^2b^3cx^9y^3z+a^2b^{15}c^8x^4y^{10 0}z$ .

Obviously all of these terms have the factors $a,b,c,x,y,z$ in common. But which ones do we take out? We take out the LEAST COMMON FACTOR. Meaning that we factor out the ones with the smallest exponents.

Let's start with a. what is the smallest exponent whch occurs with a? Well, it's 1. $a^1=a$ . So you factor out an $a$ from each term leaving you with

$a(b^2c^4x^7yz^9+ab^3cx^9y^3z+ab^{15}c^8x^4y^{100}z )$ .

And let's look at $y$ . what's the smallest exponent that occurs with $y$ ? $y^1$ ! let's do it
we already have an a out there, now will bring a y out too.

$ay(b^2c^4x^7z^9+ab^3cx^9y^22z+ab^{15}c^8x^4y^{99}z )$ .
How bout $b$ ? $b^2$ is the least common factor sooooo

$aby(bc^4x^7z^9+ab^1cx^9y^2z+ab^{13}c^8x^4y^{99}z)$ .

and you keep going until you there is nothing in common with the 3 terms anymore. REMEMBER, that is not to say that there won't be common factors in the first and second term, or the first and third, etc... No, because we aren't concerned with those. we began by factoring a TRINOMIAL not a BINOMIAL. So, always keep this in mind while factoring. Ask yourself: To what purpose am I trying to factor this expression. Is it to solve for all values of the variable, or to transform the expression so that it mimics the appearanc of another expression, etc... Don, just arbitrarily start factoring because you may end up doing more work than you had to. Well, so long, and happy math!

I'll let you do the rest.

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