243x^2 + 4158x - 6791

Question

Please help me factor this question

Answer 1

Hate to say it, but there's no way to factor this without using the quadratic equation.  When you get a problem like this, you first see if you can factor any number out (there isn't any in this case).  If you can't, then find the discriminant of the quadratic equation (b² - 4ac) to see if you'll get any "nice" whole numbers.  If not, then you will have an answer that has a square root in it, which means you can't factor it by normal means.

 

So, using the quadratic equation, we get:

 

-4158 ± √(4158²-4(243)(-6791)) / 2(243)

 

= (-4158 ± √23889816) / 486

 

= (-4158 ± 18√73734) / 486

 

= (-231 ± √73734) / 27 (divided everything by 18)

 

If you really want it in factored form, it would look like this:

 

(x - ((-231 + √73734) / 27)) (x - ((-231 - √73734) / 27))

 

Hope that helps!