SOLUTION: Factor the quadratic equation. 3x^2+13x-10 From what I know, one has to find the factors of -10, which are 2 and 5, and 10 and 1, including the negatives. After that, I think one

Question 173398: Factor the quadratic equation.
3x^2+13x-10
From what I know, one has to find the factors of -10, which are 2 and 5, and 10 and 1, including the negatives. After that, I think one has to find the sums that equal 13x, but I don't see how that would be possible.
Found 2 solutions by Mathtut, solver91311:
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
=
:

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You have only considered half of the problem. What you said is true IF the coefficient on the high order term is 1, but here it is 3.

The part about needing the factors of 10 is almost right. In fact you need the factors of -10. So, -2 and 5, 2 and -5, -1 and 10, or 1 and -10.

But the sum required to get the 13 coefficient must consider the 3 coefficient on the high order term.

, but

So

Yeah, but how do I know that a quadratic trinomial is factorable in the first place so I don't go rooting (so to speak) around for factors that might not exist? you ask.

Use the discriminant part of the quadratic formula, where a, b, and c are the coefficients of the 2nd degree, 1st degree, and constant terms respectively. If the number is a perfect square, then the quadratic is factorable, otherwise not. For the given problem, , so your example is factorable. (If you haven't done the quadratic formula yet, don't worry about it. Just use the rule above on faith for the time being)
RELATED QUESTIONS
Given the problem 2x^3-x^2-13x+10/2x+5 has a quotient of x^2-3x+1 and a remainder of 5,... (answered by Edwin McCravy)
Factor: x^4-13x^2+4 (I do not know how to put this on a formula plotting system so... (answered by KMST)
I need to find all the factors of the polynomial: 3x^3+20x^2+23x-10. I already know that... (answered by richwmiller)
Can you please tell me if i got these correct and if not which ones i got wrong thanks. (answered by KMST)
Can you please tell me if i got these correct and if not which ones i got wrong thanks. (answered by scott8148)
factor 3x^2 +13x... (answered by jim_thompson5910)
The measurement of two sides of a triangle are given {17x-7} and {3x^2+5}. The perimeter (answered by jsmallt9)
Okay, I've asked this before and still don't understand. Take the equationk (3a� - (answered by richwmiller,stanbon)
I need to know if these questions are correct thank you! 5.) Multiply (4a+x)(3a-x)... (answered by stanbon)