i need help factoring this

Question

6??^2+11??−10

 

i need to factor this, i need help

Answer 1

If you have learned the quadratic formula,   (-b ± SQRT(b²- 4ac) / 2a)  , use it when needed.  If you are systematically finding coefficients, read more.  If you are doing trial and error (an O.K. approach), then keep trying.

 

With factors (x + A)(x + B), the result is  x² + Bx + Ax + AB             [ this is F-O-I-L)

   So, find the prime factors of 6:  they are (2,3)   [used for x coefficient]

        and find the prime factors of 10  (the AB):     they are  (2,5)

        Unless we want fractions, look for a 1 and 10 or a 2 and 5 as the A and B terms  (and one negative).

 

   Now, what difference creates 11 ?     Hmmm.  seems like 2*5 - 2*2 does.    (we used the 5 and 2 of  O-I)

 

Our result is    (3x - 2)*(2x + 5)

 

p.s., I ignored the ?? and assumed an x