Answer:
Step-by-step explanation:
You want the steps involved in factoring 3x² +13x -10 by grouping.
Factors
To fill in the blanks, you need to know the product of the first and last coefficients, and the factor pairs of that product that have a sum equal to the middle coefficient.
3(-10) = -30 = (-1)(30) = (-2)(15) = (-3)(10) = (-5)(6)
The sums of these factor pairs are 29, 13, 7, 1. The sum of interest is ...
-2 + 15 = 13
These are the values that go in the first pair of blanks.
= 3x² -2 x + 15 x -10
Factors of pairs
We want to identify the common factor for each pair of terms:
= x (3x -2) + 5 (3x -2)
Factored trinomial
Finally, the common factor (3x -2) is removed and we have ...
= ( x + 5 )(3x -2)
