Factor each polynomial. See Example 7. m^4-3m^2-10

Question

Accepted Answer

Hey everyone here we are asked to factor the following polynomial of em to the fourth power minus four, M squared minus 21. Now, taking a look at our given expression here, we see that it would be rather complicated to start factoring right away since we're used to factoring expressions where the highest power is to rather than it being for like it is in this case. So we want to start by simplifying this expression and we can do this by letting the variable U be equal to m squared. So now our next step is to just rewrite our expression using this variable U. So doing this, we have U squared minus for you minus 21. And now looking at our rewritten expression, we see it is much simpler to start factoring from here. So we need to consider the factor as the quantity of a U plus B times the quantity of C. U plus D. And so now our next step is to find the values of a C and the value of B. D. And so doing this. We for starting with a C, we see that is going to be the coefficient of our first term which is just one. And then for our value for B. D. This is going to be the value of our third term which is negative 21. And so now we just need to find the factors of both of these val so starting with a C which again has the value of one. Well the factors of one are just one and one or negative one and negative one. And now for the factors of our B. D. Value which is negative 21 we have 21 negative one negative 21 positive one. We have negative seven and three or positive seven and negative three. And so now with all of these factors identified, we just need to go through a trial and error process until we find a factored form that returns our simplified expression from earlier. And so after this trial and error process we see that the factored form which returns the expression of U squared minus four U minus 21 is the quantity of U plus three times the quantity of U minus seven. And so now our last step in this problem is to just substitute back in the value for you which was M squared. So doing this, our final factored form is the quantity of M squared plus three times the quantity of M squared minus seven. And with this we have found the fully factored form of our original expression and therefore we are left with answer choice D. Thanks for watching. I hope you found this video helpful and I'll see you again next time

Factor each polynomial. See Example 7. m^4-3m^2-10

Key Concepts

Factoring Polynomials

Quadratic Form

Zero Product Property

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