Question

Factor completely: 3d^2 + d − 10.

Answer 1

The answer to your question is (d + 2)(3d - 5)

Explanation:

3d² + d - 10

Multiply the first term (3) by the third (-10) = 3 x -10 = -30

Find the prime factors of -30

-30 2

-15 3

-5 5

1

Then, -30 = 2 x 3 x 5

Find two numbers that added gives +1 and multiply gives -30. These numbers are 6 (2 x 3) and -5

Write the mid term as the addition of the numbers got.

1d = 6d - 5d

Write the polynomial as these terms

3d² + 6d - 5d - 10

Factor by grouping 3d(d + 2) - 5(d - 2)

Factor by grouping again (d + 2)(3d - 5)

Now, the polynomial is factor completely.