Question

(-x + 3x^2 + 6)(4x^2 – x), find the product of the polynomials in standard form.

A. -12x^3 + 4x^2 - 24x
B. -12x^4 + 3x^3 - 6x^2
C. -x^3 + 3x^4 + 6x
D. 12x^4 - 3x^3 + 6x^2

Answer 1

The product of the polynomials (-x + 3x^2 + 6)(4x^2 – x) in standard form is 12x^4 - 3x^3 + 25x^2 - 6x.

Step-by-step explanation:

To find the product of the polynomials (-x + 3x^2 + 6)(4x^2 – x) in standard form, we need to multiply each term of the first polynomial by each term of the second polynomial and combine like terms.

First, distribute -x to each term of the second polynomial:

-x(4x^2 – x) = -4x^3 + x^2

Then, distribute 3x^2 to each term of the second polynomial:

3x^2(4x^2 – x) = 12x^4 – 3x^3

Finally, distribute 6 to each term of the second polynomial:

6(4x^2 – x) = 24x^2 – 6x

Now, combine all the like terms to get the final polynomial:

-4x^3 + x^2 + 12x^4 – 3x^3 + 24x^2 – 6x

This simplifies to:

12x^4 - 3x^3 + 25x^2 - 6x