factor 6a^3 - 10a^2 + 3a - 5

Question

Show me the steps and answer for this question.

Answer 1

To factor the expression 6a^3 - 10a^2 + 3a - 5, we need to look for common factors among the terms.

Step 1: Group the terms in pairs:
(6a^3 - 10a^2) + (3a - 5)

Step 2: Factor out the common factors from each pair:
2a^2(3a - 5) + 1(3a - 5)

Step 3: Factor out the common factor from both terms:
(2a^2 + 1)(3a - 5)

Therefore, the factored form of 6a^3 - 10a^2 + 3a - 5 is (2a^2 + 1)(3a - 5).