Factor each polynomial. See Example 7. 10m^4+43m^2-9

Question

Accepted Answer

Hey, everyone here, we are asked to factor the following polynomial, 15 B to the fourth power plus 22 B squared minus five. Now, taking a look at our given expression here, we see that it would be sort of complicated to start factoring right away. So our first step here is to simp by our expression and we can do this by letting the variable U be equal to be squared. And so now we just want to rewrite our expression using this variable U. So we have 15 U squared plus 22 U minus five. And now looking at our simplified expression, we see it's in a format we're more familiar with. So we can go ahead and start factoring and we want to consider the factor as the quantity of A U plus B times the quantity of CU plus D. So now we need to find the factors of AC and we also need to find the factors of BD. So that means we need to first find the values of both AC and BD and AC starting with our value for AC. We see that it will be the coefficient of our first term here, which is 15 and next for hour value for BD, this is going to be the value of our third term here which is negative five. So now we just need to find the factors for both of these values starting with 15. Well, the factors of 15 are one and 15, negative one and negative 15, 3 and five and negative three and negative five. And for BD of the value of a negative five, it has the factors of one and negative five and negative one and positive five. So now all we have to do is go through some trial and error to find which combination of factors works to bring us back our simplified expression from earlier. And we find that our factored form of our simplified expression turns out to be the quantity of five U minus one times the quantity of three U plus five. And so now we just have to substitute back in our value for you, which we identified earlier. So doing this, we see that our final factored form of our original expression becomes the quantity of five B squared minus one times the quantity of three B squared plus five. And with this, we have found our fully factored form of our original expression and we are left with answer choice. A thanks for watching. I hope you found this video helpful and I'll see you again next time.

Factor each polynomial. See Example 7. 10m^4+43m^2-9

Key Concepts

Factoring Polynomials

Quadratic Form

Greatest Common Factor (GCF)

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