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factoring cubic equations

Hi, if I want to factor a cubic, say 5x3+2x2−10x 5x^3 + 2x^2 -10x and I know one factor is x=0, what's the best way to do it? My preferred was is equating coefficients to get a quadratic to then factor that, but that gives 5x2+2x−10 5x^2+2x-10 which doesn't factor so I put it through the quadratic equation and it gives irrational numbers. I know the answer is x=85 \frac{8}{5} .
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BabyMaths
Original post by gavinlee
Hi, if I want to factor a cubic, say 5x3+2x2−10x 5x^3 + 2x^2 -10x and I know one factor is x=0, what's the best way to do it? My preferred was is equating coefficients to get a quadratic to then factor that, but that gives 5x2+2x−10 5x^2+2x-10 which doesn't factor so I put it through the quadratic equation and it gives irrational numbers. I know the answer is x=85 \frac{8}{5} .


If you're solving 5x3+2x2−10x=0 5x^3 + 2x^2 -10x =0 then x=8/5 is wrong.

If you're factorising 5x3+2x2−10x 5x^3 + 2x^2 -10x then you can stop at 5x3+2x2−10x=x(5x2+2x−10) 5x^3 + 2x^2 -10x =x(5x^2+2x-10)
Original post by gavinlee
Hi, if I want to factor a cubic, say 5x3+2x2−10x 5x^3 + 2x^2 -10x and I know one factor is x=0, what's the best way to do it? My preferred was is equating coefficients to get a quadratic to then factor that, but that gives 5x2+2x−10 5x^2+2x-10 which doesn't factor so I put it through the quadratic equation and it gives irrational numbers. I know the answer is x=85 \frac{8}{5} .


Are you sure you have typed out the correct equation? I ask this because 8/5 = 1.6 is definitely not a solution.

Let's try it. If 1.6 is a solution, then 5x^3 + 2x^2 - 10x should equal 0 when entered into the calculator.

But it actually evaluates to -6.784, try it yourself.
Original post by gavinlee
Hi, if I want to factor a cubic, say 5x3+2x2−10x 5x^3 + 2x^2 -10x and I know one factor is x=0, what's the best way to do it? My preferred was is equating coefficients to get a quadratic to then factor that, but that gives 5x2+2x−10 5x^2+2x-10 which doesn't factor so I put it through the quadratic equation and it gives irrational numbers. I know the answer is x=85 \frac{8}{5} .


Are you sure the cubic isn't 5x3+2x2−16x5x^3+2x^2-16x
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gavinlee
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Original post by brianeverit
Are you sure the cubic isn't 5x3+2x2−16x5x^3+2x^2-16x



Yes sorry that's the one. I've sorted it now. :colondollar:

Thanks to all the above posters.

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