Factor completely:

Question

Factor completely:

x^{3} + x^{2} - 4 x - 4.

Accepted Answer

Welcome back. I'm so glad you're here. We've got these four terms X cubed minus five, X squared minus nine, X plus 45 we are asked to factor completely. Well when we've got four terms like this, we can give it a go with factoring by grouping, we can choose to group these first two terms and group the second two terms and see if they have any factors in common. The first two terms X to the third minus five, X squared. They both have an X squared in them. X to the third divided by X squared. Leaves us with X negative five, X squared divided by X squared. Leaves us with negative five. In the second two terms negative nine X plus 45. They both have a negative nine in them. And so we can factor out a negative nine. Negative nine X divided by negative nine Leaves us with X and 45 divided by negative nine Leaves us with negative five. And hey look it worked, they do have a factor in common this x minus five and so we can factor that out. We've now got x minus five times X squared minus nine. And cool, but we're not done yet because we notice that this x squared minus nine. Well that is a difference of squares. So we recall from previous lessons that a difference of squares is when you have a squared minus B squared and in this case the x squared, well X A equals X and the B squared. Well what times what is nine? That's three. So we've got x squared minus three squared and B equals three. So how do we factor a difference of squares? We're going to have A plus B times a minus B. And in this case that would be a X plus B is three times x minus three. Well, great. We'll go back over here and copy this down. We've got x minus five times now. X plus three times X minus three. And that is as factored as that one is going to get we look at our answer choices in this matches with answer choice C. Well done, we'll catch you on the next one.

Factor completely: $x^{3} + x^{2} - 4 x - 4.$

Key Concepts

Factoring Polynomials

Rational Root Theorem

Synthetic Division

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