Question

what is the difference of the two polynomials?
$(9x^2 + 8x) - (2x^2 + 3x)$
$\bigcirc\\ 7x^2 + 5x$
$\bigcirc\\ 7x^2 + 11x$
$\bigcirc\\ 11x^2 + 5x$
$\bigcirc\\ 11x^2 + 11x$

Explanation:

Step1: Distribute the negative sign

To subtract the second polynomial from the first, we distribute the negative sign to each term in the second polynomial:
$$(9x^2 + 8x) - (2x^2 + 3x) = 9x^2 + 8x - 2x^2 - 3x$$

Step2: Combine like terms

Next, we combine the like terms (the \(x^2\) terms and the \(x\) terms):
For the \(x^2\) terms: \(9x^2 - 2x^2 = 7x^2\)
For the \(x\) terms: \(8x - 3x = 5x\)
Putting these together, we get:
$$7x^2 + 5x$$

Answer:

A. \(7x^2 + 5x\)