# Rational Zeros of a function

• Apr 20th 2012, 12:36 AM
iFuuZe
Rational Zeros of a function
Find all rational zeros of the function:

f(x)=25x^4+25x^3-154x^2-4x+24

ok i found the two zeros 2 and -3, now i dont know how to factor it please help i dont understand how to get the answear

(x-2)(x+3) (.....
• Apr 20th 2012, 12:39 AM
a tutor
Re: Rational Zeros of a function
Multiply the two that you found to get x^2+x-6 and then divide by that.

I can't teach you polynomial division on here but you could choose a video from here..

• Apr 20th 2012, 02:48 AM
iFuuZe
Re: Rational Zeros of a function
hey yep i did long division and got -8x as a remainder, how do i procede??
• Apr 20th 2012, 03:03 AM
a tutor
Re: Rational Zeros of a function
Did you watch one of the videos?
• Apr 20th 2012, 04:01 AM
iFuuZe
Re: Rational Zeros of a function
Top line 25x^2-4 how do i prosede??
• Apr 20th 2012, 04:09 AM
a tutor
Re: Rational Zeros of a function
Yes that's correct. Now factorise 25x^2-4. It's a difference of two squares.

&#40;25x&#94;4&#43;25x&#94;3-154x&#94;2-4x&#43;24&#41;&#47;&#40;x&#94;2&#43;x-6&#41; - Wolfram|Alpha
• Apr 20th 2012, 04:14 AM
iFuuZe
Re: Rational Zeros of a function
i dont really get the website. Now you get (5x-2)(5x+2) what i do next??
• Apr 20th 2012, 04:21 AM
a tutor
Re: Rational Zeros of a function
So now you have $(x-2)(x+3)(5x-2)(5x+2)=0$.

The product will be zero whenever one of the factors is zero.
• Apr 20th 2012, 04:25 AM
biffboy
Re: Rational Zeros of a function
You now have (x-2)(x+3)(5x-2)(5x+2)=0 So x=2 or -3 or 2/5 or -2/5
• Apr 20th 2012, 04:38 AM
iFuuZe
Re: Rational Zeros of a function
does this question have anything to do with imagenery numbers