Answer
$(3x + 5)(x - 2)$
Work Step by Step
Factor $3x^{2}-x-10$
First set up the x's in the binomial.
$(cx +or- n)(cx +or- n)$
To have $3x^{2}$ in the original equation the two $x$'s in the binomial multiply together. Thus the $x$'s have coefficients.
3 is a prime number so its only factors are 3 and 1. Therefore in one of the parentheses the $x$ has a coefficient of 3 and the other has a coefficient of 1
$(3x +or- n)(1x +or- n)$
Now we need to find n in the expression above
both n values must multiply to -10 and add (when the expression is expanded) -1x.
Also we must take into account the 3 coefficient.
To start list out the factors of -10:
-1,10
1,-10
-2,5
2,5
Think which of these factor pairs when one number is multiplied by three and subtracted by the other leaves us with -1
Immediately we can discount the 1,10 pairs because there would be too large of a difference, leaving us to choose between the -2,5 and the 2,-5 factor pairs.
$2*3=6$ and $5-6=1$ so we know that the $2$ will not be in the same parentheses as the $3x$
$(3x +or- 5)(1x +or- 2)$
Last we need to figure out the signs within the parentheses. As mentioned before $5-6=1$ so we want 6 to be negative, thus we write $-2$
$(3x +or- 5)(1x - 2)$
And because we want 5 to be positive we write $+5$
$(3x + 5)(x - 2)$
To check expand the expression and will match the original equation
