In Exercises 1–68, factor completely, or state that the polynomia...

Question

In Exercises 1–68, factor completely, or state that the polynomial is prime. x² − 12x + 36 − 49y²

Accepted Answer

Hello, everyone. We've been asked to perform a complete factorization of the given expression or categorize it as the prime polynomial. The expression we're given is M squared minus 25 M plus 27 minus 81 N squared. Our answer choices are a, the parentheses M -25 multiplied by the parentheses, 1 -9 N B. The parentheses M plus 25 multiplied by the parentheses, one minus nine N C. The parentheses M minus 25 multiplied by the parentheses. One plus nine N D. The given polynomial is prime rewriting my original expression M squared minus 25 M Plus 27 -81 N Squared. All right. So I will start by looking for a greatest common factor. See if there's anything that's the same through all four terms that I can factor out. There is not a seam variable for all four and there is no common coefficient. So the next thing I try when I have four terms is I usually try to factor by grouping. I recall that when I factor by grouping I group two terms together in one set of parentheses and two terms together in another set of parentheses. So I have parentheses around M squared minus 25 M in parentheses around 27 -81 n squared. So now I'm gonna see if there is a greatest common factor within my new parentheses that I can factor out. So the greatest common factor for M squared minus 25 M would be M. So I write that open parentheses, then divide each of those terms by M. So M squared divided by M is M minus M divided by M is a minus or sorry, negative 25 closed parentheses. My next set of grouping or parentheses. I have 27 -81 n squared. I'm looking for a greatest common factor and actually, I think 27 is my greatest common factor. So I'm gonna put a plus sign 27 open parentheses and then 27 divided by 27 is -81 n squared, divided by 27 is negative three N squared. So at this step, I have M multiplied by the parentheses. M minus 25 closed parentheses plus 27 multiplied by the parentheses, one minus three N squared, closed parentheses. For this to be factor by grouping. I need a binomial common factor. And my parentheses here do not match. There is no binomial, greatest common factor in this case. So there's nothing else I can do with this problem and truly can't really factor it. So the answer choice D the given polynomial is prime, is the correct answer. Have a nice day.

Struggling with College Algebra?

In Exercises 1–68, factor completely, or state that the polynomial is prime. x² − 12x + 36 − 49y²

Watch next

Factoring Polynomials practice set