# Thread: factorising

1. ## factorising

2x^2+5x+1

can this be factorised?

2. Sure it is, but since you're asking I'm assuming that you mean over the reals and probably without using radicals. In that case, no.

3. it must! there's a remainder of 3 from the expression i divided by (x-1)

but it's not part of the quadratic..

4. Originally Posted by x-disturbed-x
2x^2+5x+1

can this be factorised?
Suppose it can be factorised then we would have:

$2x^2+5x+1=2(x-a)(x-b)$,

for some $a$ and $b$. But when $x=a$, or $x=b$
the RHS of the last equation is zero.

Therefore $b$ and $c$ are the roots of the quadratic
on the LHS.

The quadratic formula will give the roots of $2x^2+5x+1$,
which will then allow you to factorise this quadratic.

RonL

5. captainblack! you scare me with talk of RHS. there must be an easier way

6. Actually it's pretty simple simply plug in the values of

A=2
B=5
C=1

into the quadratic equation

7. A quadratic equation always has 2 roots, if the discriminant is positive, you have two distinct real zeroes, let's call them a and b. You can then always factor (x-a)(x-b). You can find a and b by using the quadratic formula, as CaptainBlack suggested.