Question

2. Fill in the blanks to factor the trinomial 3x² + 13x - 10 by grouping.

3x² + 13x - 10 = 3x² -
=
3x²-x+.
_X+X-10
(3x - 2) +(3x - 2)
+
)(3x - 2)

Answer 1

• -2 and 15
• x and 5
• x and 5

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)