Factor each polynomial completely. See Example 6. 40ab - 16a

Question

Accepted Answer

Hey, everyone here we are asked to rewrite the following expression by factoring it completely. Here we are given 63 MN minus 27 M. Here we have four answer choice options, answer choice A seven N multiplied by three M minus nine. Answer B nine M multiplied by seven N minus three. Answer C three M multiplied by seven N minus three and answer D seven N multiplied by nine M minus three. So to begin factoring our given expression, we first want to begin by assessing our coefficients for both of the terms. So for our first term, we have the coefficient of 63. And then for our second term, we have the coefficient of 27 and we can neglect the negative or minus sign for now. So we have just 27 and now we just want to find the greatest common factor between both of these coefficients. So we will start with the smallest value which is 27. And we want to first factor out the largest possible value from 27 which in this case is nine because we know nine times three gives us 27. So now we just want to confirm that we can also factor out nine from our other coefficient. So now looking at 63 we can recall that nine times seven gives us 63. So this tells us that our greatest common factor for our coefficients is nine. So we can factor out nine from both of the terms. Now, looking back at our given expression, we can notice that both of the terms both contain the variable M. So we can factor out this common variable from both of the terms. So in total here we are going to be factoring out nine N and when we factor out nine M, this leaves us with the two terms which are seven N and minus three. So in summary, here we have answer choice B where our factored expression is nine M multiplied by the remaining expression which is seven N minus three. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Factor each polynomial completely. See Example 6. 40ab - 16a

Key Concepts

Greatest Common Factor (GCF)

Factoring Polynomials

Properties of Variables and Exponents

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