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Please help!Use synthetic division and the given fact to solve the fallowing equation. x^3+4x^2-17x-60=0; (x-4)

User Alex Coppock
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1 Answer

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22 votes

From the given facts, x-4 is a root of our polynomial, then we can compute the synthetic division of our polynomial by x-4, that is

Let's compute the synthetic division,

then, our division leads to

Now, we can note that the quadratic polynomial can be written as


x^2+8x+15=(x+3)(x+5)

Then, our given polynomial is equal to


x^3+4x^2-17x-60=(x-4)(x+3)(x+5)

So, we need to solve


(x-4)(x+3)(x+5)=0

Therefore, the solutions are


\begin{gathered} x=4 \\ x=-3 \\ x=-5 \end{gathered}

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User Guimoute
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