Hi there, any help on these two questions would be muchly appreciated. Im trying to use Factor Theorem to answer a few questions, I've been successful up until these last two questions.
Factorise:
1)
and
2)
Thanks.
For the first one, you could try dividing it by some possible roots, like -1, -4, or 3/2. Try dividing by (x+1), (x+4) or (2x-3). If it reduces to a quadratic by dividing by either of those, then you are in business.
You could also rewrite this one as
...............7x^2..........-7x
Factor:
For the second one, same logic as before. Try dividing this one by (x-3), x-2, or x+2. It should reduce to a quadratic and be easy thereafter. Okey-doke?.
Hello, Nick87!
The Factor Theorem has two powerful features:
Given a polynomial
if , then is a factor of
The only rational zeros of are of the form
. . where is a factor of the constant term and is a factor of the leading coefficient.
I'm using the Factor Theorem.
I've been successful up until these last two questions.
The factors of the constant term are: .
The factors of the leading coefficient are: .
The possible rational zeros are: .
We find that: .
But: .
. . Since is a zero, then is a factor.
Using long (or synthetic division): .
. . Therefore: .
The possible zeros are: .
We find that: .
. . Hence, is a factor.
. . and we have: .
Therefore: .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
This one could have been factored "by grouping" . . .
. .
. .