# Algebra

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I am trying to factor polynomials by grouping the first two terms and the last two terms, but I am having some issues, I have done a few correct since I can look at the answers to the odd problems but it is taking me arund 25 minutes per problem. here is a sample problem in hope someone can explain it to be better than my book.
x to the 5th power + x cubed -2x squared-2

x^5 + x^3 - 2x^2 - 2

x^3 is a common factor in the first two terms and the 2 is the only common factor in the last two.

x^3(x^2 + 1) ....

now look at the last two, they are both negative while the stuff at the front is positive. So the clue would be to factor out a -2

so
x^3(x^2 + 1) - 2(x^2 + 1)

you now have two terms with x^2 + 1 as a new common factor

so to finish it off:

Notice that if we expand our answer, we get back the original expression, so our answer is correct.

These questions take practise and you might have to re-arrange the terms into groups that belong together

ok, so if I had x^3-4x^2+2x-8
in the first 2 terms x^3-4x^2; x^2 is my common factor and in the second set of terms 2x-8, 2 is my common factor.
so it would look like this:
(x^2+4)(x-2)
correct?

But what if I had this....2x-10+xy-5y?
in my first to terms 2x-10 2 is the common factor right? and in the second y is my common factor correct?

I just noticed that was wrong.
it should be (x-5)(2-y).

No.
for

x^3-4x^2+2x-8
=x^2(x-4) + 2(x-4)
= (x - 4)(x^2 + 2)

again no, and also no for your correction.

Here is the step-by-step

2x-10+xy-5y
= 2(x-5) + y(x-5) notice (x-5) is the new common factor

=(x-5)(2+y)

Are you not writing down the second lines in your solutions?
From that it would be obvious why it is +y and not -y

Thanks, I am messing up my signs it looks like. But it looks like i have factored correctly. I will continue to practice, thanks for your help.

• Algebra -

123=3

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