Question

What is the standard polynomial form of (4x^2+3x) . (x^2-8) cdot (6x+15)?

a) (24x^5 - 150x^4 - 47x^3 + 303x^2 - 360x - 360)
b) (24x^5 - 150x^4 - 47x^3 + 303x^2 + 360x - 360)
c) (24x^5 - 150x^4 - 47x^3 - 303x^2 - 360x - 360)
d) (24x^5 - 150x^4 + 47x^3 + 303x^2 - 360x - 360)

Answer 1

The standard polynomial form of (4x^2+3x) . (x^2-8) ⋅ (6x+15) is (24x^5 - 150x^4 - 47x^3 + 303x^2 - 360x - 360).

Step-by-step explanation:

The student is asking for the standard polynomial form of the given expression, which involves multiplying polynomial expressions together. The expressions to multiply are (4x^2+3x), (x^2-8), and (6x+15). To find the standard form, we perform polynomial multiplication step by step.

Multiply (4x^2+3x) and (x^2-8) to get 4x^4 - 32x^2 + 3x^3 - 24x.

Multiply the result from step 1 by (6x+15), distributing each term of the first polynomial across each term of the second polynomial.

Combine like terms and arrange the terms in descending powers of x to achieve the standard polynomial form.

After performing these steps, the correct standard polynomial form is option (a): (24x^5 - 150x^4 - 47x^3 + 303x^2 - 360x - 360).