Question

Factoring polynomials:
f(x)=x^3 +10x^2 +25x

I know I can take out the x but I just need a little direction from there to get to the way it is set up on my papers :)

Answer 1

It'd help others help you if you'd demonstrate "the way it is set up on [your] papers."

Answer 2

\[f(x)=x^3+10x^2+25x\]Put x in evidence\[f(x)=x*(x^2+10x+25)\]\[\boxed{f(x)=x*(x+5)^2}\]

Answer 3

@D3xt3R: "in evidence" ??? plese explain what you mean there.

Answer 4

Thanks D3xt3r That's what I thought it was but I just didn't see how the 10x was for lack of a better word erased from the equation

Answer 5

Sorry, I'll rewrite my answer.

Answer 6

It's cool

Answer 7

@mathmale I'm sorry about my mistake, I'm trying to improve my english here ;)

\[f(x)=x^3+10x^2+25x\] Now we have to take of a single X of the function (I don't know how can i speak it in English, sorry)
\[f(x)=x*(x^2+10x+25)\]
\[f(x)=x*(x+5)^2\]

Answer 8

factor out an x ....

Answer 9

if you can determine the roots of the equation, that is when f(x) = 0, then this reduces to what you were doing before

Answer 10

Thanks @amistre64 ;D

Answer 11

:) youre welcome

Answer 12

\[In~ the ~function~ f(x)=x^3+10x^2+25x\]every term on the right involves x to the first power, and thus we say "x is a factor common to all three terms" and we can thus factor it out. What's left is \[f(x)=x(x^2+10x+25).\] Now, \[x^2+10x+25\]is a perfect square and is equivalent to (x+5)^2.
Thus, the given function, in fully factored form, is\[f(x)=x(x+5)^2.\]the roots of this functin are x=0 and x=-5; x=-5 has a "multiplicity" of 2, because the factor (x+5) shows up twice.

Hope this discussion helps a bit with the vocabulary.

Answer 13

Thanks all

Answer 14

Thanks @mathmale