Q. 452

Factor completely:

$6 x^{2} - 11 x - 10 .$

Verified

Answer

The factored polynomial is,

$(2 x - 5) (3 x + 2)$ .

1Step 1. Given the information.

The polynomial function is,

$6 x^{2} - 11 x - 10$ .

2Step 2. Factoring the polynomail.

$6 x^{2} - 11 x - 10$

Splitting the middle term such that the sum of the terms is $(- 11)$ and the product of the terms is $(- 60)$ .

$= 6 x^{2} - 15 x + 4 x - 10 = (6 x^{2} - 15 x) + (4 x - 10)$

Taking out the common factors,

$= 3 x (2 x - 5) + 2 (2 x - 5) = (3 x + 2) (2 x - 5)$

3Step 3. Checking the solution.

$(3 x + 2) (2 x - 5)$

Multiplying the brackets,

$= 3 x (2 x - 5) + 2 (2 x - 5) = 6 x^{2} - 15 x + 4 x - 10 = 6 x^{2} - 11 x - 10$

This is true.