Question

How would you factorize the polynomial expression 24x^3 - 64x^2 - 21x + 56, and what are the steps involved in factoring this expression?

Answer 1

To factor the polynomial, group terms with common factors. Factor out the greatest common factor from each group then factor out the common binomial. The factored form is: (3x - 8)(8x^2 - 7).

Step-by-step explanation:

Factoring the given polynomial, 24x^3 - 64x^2 - 21x + 56, involves several steps:

1. Group terms which have common factors: 24x^3 - 64x^2 can be grouped together, and - 21x + 56 can be grouped together.
2. Factor out the greatest common factor (GCF) in each group: 24x^3 - 64x^2 becomes 8x^2(3x - 8) and - 21x + 56 becomes -7(3x -8).
3. The expression now becomes: 8x^2(3x - 8) - 7(3x-8).
4. Now you can see a common factor of (3x - 8) in both parts of the expression, so you can factor that out, leaving you with (3x - 8)(8x^2 - 7).

So, the factored form of the polynomial 24x^3 - 64x^2 - 21x + 56 is (3x - 8)(8x^2 - 7).

Learn more about Factoring Polynomials