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Chapter 0: Problem 16

Factor by grouping. $$x^{3}-x^{2}-5 x+5$$

Short Answer

Expert verified
The factorized form of the given cubic polynomial \(x^{3}-x^{2}-5x+5\) by method of grouping is \((x^{2}-5)(x-1)\)

Step by step solution

01

Re-arrange polynomial

Firstly, rearrange the given cubic polynomial in a way that we could apply the method of grouping effectively. Rearrange the polynomial in such a way that it might look like \(x^3-5x+(-x^2+5)\). Here we just separated the last two terms.
02

Factor by grouping

Now, by method of grouping, take out common monomial factor from each group. From the first group \(x(x^2-5)\) and from the second group, -1 can be taken out as common, resulting in \(-1(x^2-5)\)
03

Simplify the result

On observing the resulting expression, \(x(x^2-5) -1(x^2-5)\), we can see \(x^2 - 5\) is a common binomial factor. Take out \(x^2 - 5\) as common and we have \((x^2-5)(x-1)\) as the factorized form of the given cubic polynomial.

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Most popular questions from this chapter

In solving \(\sqrt{2 x-1}+2=x,\) why is it a good idea to isolate the radical term? What if we don't do this and simply square each side? Describe what happens.

What is a quadratic equation?

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