Factor each trinomial, if possible. See Examples 3 and 4. 8h^2-2h...

Question

Factor each trinomial, if possible. See Examples 3 and 4. 8h^2-2h-21

Accepted Answer

Hello. Everyone in this video we're going to be looking at this practice problem. We're going to factor the polynomial six H squared minus 13 H minus five. So in this case we're going to be working on factoring a try no me in where the leading term is not one but six. So that means that we're looking for the first terms of our factors to multiply 26 H squared. So because I'm factoring, I know that there's going to be At least two terms and the first the first term within those factors have to multiply to get sit six H squared. So when I think of numbers that multiply to get me six H squared, there's two H times three H Or one H times six h and of course negative two H times negative three H. Is also equal to six H squared. Because two negatives make a positive. So that means that all of these factors I can also include in their negative form. As long as both of the terms are negative. So for this case I'm just gonna try one H Times six H. And then I can go ahead and add the second term. Well I know that the last term of my polynomial is negative five which means that the last terms of my factors have to multiply to give me -5. So I can get negative five by multiplying positive one with negative five or negative one with positive five. So those are all the factory authorizations that could work. And for this first child I will do plus one plus negative five And realize I say trial. Because there's a couple of different combinations that we can try to get the right answer. But now that I've written out this first one where I have H plus one times six H minus five. I can multiply it out and see if I get back my original polynomial. So I do that. I can do H. Times six. H. Is six. H squared H. Times negative five is negative five H. Positive one times 6. H. is positive six. H. And positive one times negative five is negative five. So now my polynomial is six H squared negative five. H plus six. H. Is positive H minus five. And from here you can see that the polynomial I get back from this combination is not the same as my original polynomial. So this combination is not the right one. So I can go ahead and try a different one. So I will try two H. Plus one times three H -5. So if I try this, I have two H. Times three ages six H squared two H times negative five is negative 10 H. Three positive three times three H. S. Plus three H. And positive three times negative five is negative five. So I can combine the middle terms. So I have two H squared negative 10 H. Plus three H. Is negative seven H minus five. And once again you can see that this is also not the same as our original polynomial. But we are getting closer because this middle term is negative. So I'm gonna play around with those factors. I'll switch the order. So I'll do three h plus one Times two H -5. So if I do this I have three H. Times two H. Is six. H squared three H times negative five is negative 15. H. One times two H. Is positive two H. And one times negative five is negative five. And again if I combine the middle terms negative 15 H plus two H. Is negative 13 H. So I have six H squared minus five. And if we look at this polynomial versus the original, you can see that we have the same polynomial. So this factory Ization works for us, which means that three H plus one times two H minus five is our final factory Ization. And you can see that that aligns with answer choice D. So hopefully this video helped and see you next time.

Factor each trinomial, if possible. See Examples 3 and 4. 8h^2-2h-21

Key Concepts

Factoring Trinomials

The Distributive Property

Identifying Coefficients and Constants

Watch next