# Thread: How do I find the linear factor?

1. ## How do I find the linear factor?

Find the linear factor of the form x-a, when a is a constant, of the cubic polynomial

$\displaystyle f(x) = x^3+2x^2+2x +4$ and hence factorise f(x)

2. Begin by grouping the terms like this

$\displaystyle (x^3+2x^2)+(2x+4)$

now factor

$\displaystyle x^2(x+2)+2(x+2)$

You can see that (x+2) is a factor of both terms, and now it can be fatored out like so

$\displaystyle (x+2)(x^2+2)$

Does that help? There are alot of ways to approach expressions of degree>2. Your goal is to know them all and to be able to know when is the right time to use the appropriate method.

Oh, I almost forgot. You need the linear factor in the form (x-a), but x+2=x-(-2), therefore a=-2

Got it?

3. Originally Posted by gva0324
$\displaystyle f(x) = x^3+2x^2+2x +4$ and hence factorise f(x)
The constant $\displaystyle a$ is where $\displaystyle f(a)=0.$ Good candidates to try for $\displaystyle a$ are the divisors of the constant term, in this case $\displaystyle \pm1,\,\pm2,\,\pm4.$ You can also look at the polynomial and make a few eliminations. In this case, all the coefficients are positive, so you must try a negative number. Also all but one of the coefficients are even, so $\displaystyle \pm1$ are no good. Therefore, you should try $\displaystyle f(-2)$ and $\displaystyle f(-4)$ and see which is 0.