Question

Reduce 15x^5 + 20x^4 - 6x^3 - 8x^2.

a) 5x^2 + 2x - 1
b) 3x^3 + 4x^2 - 2x - 4
c) 5x^3 - 4x^2 + 2x + 4
d) 3x^2 - 4x + 2

Answer 1

The polynomial 15x^5 + 20x^4 - 6x^3 - 8x^2 is already in its reduced form. There are no like terms to combine, and factoring out the GCF does not simplify the expression further. None of the provided answer choices are correct.

Step-by-step explanation:

The question asks to reduce the polynomial 15x^5 + 20x^4 - 6x^3 - 8x^2. Reducing a polynomial typically involves factoring out the greatest common factor (GCF) from its terms. In this case, the GCF for all the terms in the polynomial is 3x^2.

Let's factor out the GCF:

3x^2(5x^3 + ​ ​(20/3)x^2 - 2x - ​ ​(8/3))

This simplifies to:

3x^2(5x^3 + ​ ​(20/3)x^2 - 2x - ​ ​(8/3)) = 3x^2(5x^3 + ​ ​(20/3)x^2 - 2x - ​ ​(8/3))

But, upon re-examination, it seems there was a misunderstanding: The task doesn't simply involve factoring out the GCF; we actually need to reduce the polynomial by combining like terms or simplifying expressions within it. However, there are no like terms to combine in the given polynomial, and no simplification is possible beyond this. Therefore, the polynomial is already in its reduced form.

The original expression 15x^5 + 20x^4 - 6x^3 - 8x^2 is the reduced form and none of the answer choices (a), (b), (c), or (d) correctly represent the reduced form of the given polynomial.