Question 374311
How to factor:
{{{5x^2+34x+24}}}
To factor this trinomial, you need to find two binomials which, when multiplied, will give you the original trinomial.
In other words, find {{{(ax+m)}}} and {{{(bx+n)}}} such that {{{(ax+m)(bx+n) = 5x^2+34x+24}}}
First, you look at the coefficient of {{{x^2}}}, and that's 5.
Now ask what are the factors of 5?
Well, 5 is a prime number, so the factors are 1 and 5.
So you can start with:
{{{(5x+m)(x+n)}}} Notice the {{{a=5}}} and {{{b = 1}}}
Now look at the constant term, that's 24.
You need to find the two integers, m and n, whose product is 24 and whose sum 5*n+1*m = 34.
Let's factor 24.
1X24 = 24
2X12 = 24
3X8 = 24
4X6 = 24
After a little trial & error, you'll find:
5*6+1*4 = 34
So this means that n = 6 and m = 4
Now you can finish by writing:
{{{highlight(5x^2+34x+24 = (5x+4)(x+6))}}}