Question

Let P be a polynomial where P(x) = (x + 6) (x + 3) (x – 5). Rewrite the polynomial in standard form (in other words, multiply the parentheses).

a. P(x) = x³ + 4x² - 15x - 90
b. P(x) = x³ - 6x² - 9x + 30
c. P(x) = x³ + 3x² - 30x - 90
d. P(x) = x³ + 9x² - 30x - 90

Answer 1

To find the standard form of the polynomial P(x) = (x + 6) (x + 3) (x - 5), polynomial multiplication is performed step by step, simplifying the result to P(x) = x^3 + 4x^2 - 27x - 90.

Step-by-step explanation:

To rewrite the polynomial P(x) = (x + 6) (x + 3) (x - 5) in standard form, we need to perform polynomial multiplication. Let's break it down step by step:

1. First, multiply the binomials (x + 6) and (x + 3):

(x + 6)(x + 3) = x2 + 3x + 6x + 18 = x2 + 9x + 18

1. Next, multiply this result by the binomial (x - 5):

(x2 + 9x + 18)(x - 5) = x3 - 5x2 + 9x2 - 45x + 18x - 90

Simplify by combining like terms:

x3 + 4x2 - 27x - 90

The polynomial in standard form is P(x) = x3 + 4x2 - 27x - 90, which corresponds to option (a).