Final answer:
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:
- Group terms which have common factors: 24x^3 - 64x^2 can be grouped together, and - 21x + 56 can be grouped together.
- 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).
- The expression now becomes: 8x^2(3x - 8) - 7(3x-8).
- 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