In Exercises 65–92, factor completely, or state that the polynomi...

Question

In Exercises 65–92, factor completely, or state that the polynomial is prime. 6x^2−6x−12

Accepted Answer

Hello today we're gonna be factoring a polynomial. So the polynomial given to us is five X squared plus 15 X minus 20. Now, if we take a look at the coefficients of the three terms given to us, the coefficients are 5, 15 and 20 and all three of these coefficients are divisible by five. So this try no mia will currently has the greatest common factor of five. So what we can go ahead and do in order to simplify this polynomial is factor out of five from the entire thing. Doing so is going to give us five times the quantity X squared plus three x minus four. Now what we want to go ahead and do is factor this trin Amiel while the coefficient of the first term is one. So what we want to go ahead and do is find two factors of the last term that can multiply together to give us negative four but add up to give us positive three. While those two factors are going to be positive four and negative 14 times negative one gives us negative four and four plus negative one gives us positive three. That means that this try no meal is going to factor to five times the quantities X plus four times x minus one. And this is going to be the fully factored version of our given polynomial. That also means that the answer to this problem is going to be d. So I hope this video helps you in understanding how to factor this type of polynomial and I'll go ahead and see you all in the next video.

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