Factor each polynomial completely. See Example 6. 6ar + 12br -...

Question

Factor each polynomial completely. See Example 6. 6ar + 12br - 5as - 10bs

Accepted Answer

Welcome back, everyone. In this problem, we want to rewrite the expression four MP plus 12 NP minus three MQ minus nine NQ by factoring it completely for our answer choices. A is the product of three P minus four, Q and M plus three NB is the product of four P minus three, Q and M plus three N C is the product of three P minus four Q and three M plus N and D is the product of four P minus three Q and three M plus N. Now, what do we know? Well, we know that if we have from our expression here. So four MP plus 12 NP minus three MQ minus nine NQ. All right. My Q is a little bit fancy. Don't watch me. We notice that there are no common factors across all four terms. However, there are common factors within the groups of two. So if we can group or common factors, then we should be able to see if we can find a common factor among all. So let's go ahead and do that. Now, what's the common factor between four MP and 12 NP? Well, four NP are common And if I factor out four P factor and four P from four MP leaves me with M and four P out of NP leaves me with three N. Likewise, for negative three MQ minus nine NQ, negative three Q is a common factor. So if I write that, if I factor on negative three Q negative three Q factor from negative three MQ gives me a positive M a negative three Q factor out of nine, negative nine NQ gives us a positive three N. And just to expand on that, if you think about it factoring negative three Q from negative nine NQ, then negative three into negative nine goes positive three times and we can cancel out Q. So that's how we got that to be equal to three N. I just thought I'd point to it because sometimes students make mistakes in factoring out a negative from another negative term. They may not remember to that. A negative factor from a negative is a positive. So I thought I'd just add that. No, if we notice here, we have two common factors. Both of them have a factor of M plus three N. That means we can combine the terms on the outside, which is four P minus three Q and M plus three N. No, we have factored it completely and that would have been answer choice. B thanks a lot for watching everyone. I hope this video helped.

Factor each polynomial completely. See Example 6. 6ar + 12br - 5as - 10bs

Key Concepts

Factoring by Grouping

Greatest Common Factor (GCF)

Distributive Property

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