Question

Question p(x)=4x³ - 2x² - 3x q(x) = 5 - x - x³ If p(x) and q(x) are polynomials as defined above, what is p(x) + 2q(x) ? 3x³ - 6x + 10 2x³ - 3x² + 10 3x³ - 2x² - 3x + 10 2x³ - 2x² - 5x + 10

Answer 1

To find p(x) + 2q(x), we add the polynomial p(x) to twice the polynomial q(x) and then combine like terms. The result is the polynomial 2x³ - 2x² - 5x + 10.

Step-by-step explanation:

To find the polynomial p(x) + 2q(x), we need to first determine p(x) and 2q(x), and then combine like terms. The polynomials are:

p(x) = 4x³ - 2x² - 3x

q(x) = 5 - x - x³

To get 2q(x), simply multiply each term in q(x) by 2:

2q(x) = 2(5 - x - x³) = 10 - 2x - 2x³

Now we add p(x) and 2q(x):

p(x) + 2q(x) = (4x³ - 2x² - 3x) + (10 - 2x - 2x³)

Combine like terms:

p(x) + 2q(x) = 4x³ - 2x³ - 2x² - 3x - 2x + 10

p(x) + 2q(x) = 2x³ - 2x² - 5x + 10

Therefore, the solution is 2x³ - 2x² - 5x + 10.