Factor each trinomial, if possible. See Examples 3 and 4. 9x^2+4x...

Question

Factor each trinomial, if possible. See Examples 3 and 4. 9x^2+4x-2

Accepted Answer

Hello everyone in this video we're going to be looking at this practice problem where we want to factor the polynomial seven X squared plus five X minus three. So in this case in order to factor this polynomial you can observe that the polynomial follows the quadratic equation formula which is a X squared, let's be X plus C. And when we're factoring a quadratic equation we want to find a term that when A. And C are multiplied together, the terms the two terms that we find two factor equal that amount. And we want those two terms to also add to get the value of B. So we're going to sort of use this as a guideline to see if it can help us factor this polynomial. And if we compare seven X squared plus five X minus three to the quadratic equation you can see that A is equal to seven. B is equal to five and C is equal to -3. So in this case a time C is equal to 21 and B is equal to five. So I want to find two terms that multiply to get But add to get five. Well the factors of 21 is either one and 21 and there's no way that subtracting one from 21 is going to get me five or adding 1 to 21 is going to get me five. So I know that's not an option and the next option is three and seven. So if I add three and seven together I get 10 which is not five. If I subtract seven from three I get negative four which is still not five. So I can try switching this seven minus three is now positive four. So still not five. So it seems like there really is no way to factor this. So our next option could be to try and see the other options or the answer choices. So if we look at answer choice A there's x minus one times seven X plus three. Well we can check if this is the correct factory ization by multiplying it again and seeing if we get the original polynomial back. So if I multiply this, I can use the foil method. So I'll multiply the first terms together X times seven X is seven X squared. Then I'll do the outer terms X times three. Here's three X. The inner terms negative one times seven X is negative seven X. And lastly the last terms -1, Times three is -3. These middle terms are like terms, so I can combine them when I do that I get seven X squared minus four x minus three. And this does not equal the original polynomial. So I know that A is not an option. Now we can look at B and do the same. So B is seven x minus one times X plus three. And again if we multiply this I get seven X squared Plus 21, X minus X minus three. The middle terms combined again. So I have seven X squared plus 20 X. Because 21 x minus x is 20 x minus three. And once again this does not equal the original polynomial, so B is also not an option. And finally we can check C. Which is seven X plus one times x minus three. I do the foil method. Again, I have seven X times X. So seven X squared. Then seven X times negative three is negative X. And then one times X is X. And one times negative three is negative three, combining those middle terms. Again, I have seven x squared minus 20 X. Because negative 21 X plus X is negative 20 X minus three. And once again this does not equal the original equation. So as we suspected this factory ization is not possible both in the way that we checked all the answer choices. And we determined that There's no factor that multiplies to 21 But gets us but adds to five. So hopefully this video helped and see you next time

Factor each trinomial, if possible. See Examples 3 and 4. 9x^2+4x-2

Key Concepts

Factoring Trinomials

Quadratic Formula

Discriminant

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