Question

what is the difference of the polynomials?
$(5x^3 + 4x^2) - (6x^2 - 2x - 9)$
options:
$-x^3 + 6x^2 + 9$
$-x^3 + 2x^2 - 9$
$5x^3 - 2x^2 - 2x - 9$
$5x^3 - 2x^2 + 2x + 9$

Explanation:

Step1: Distribute the negative sign

To subtract the polynomial \( (6x^2 - 2x - 9) \) from \( (5x^3 + 4x^2) \), we distribute the negative sign to each term inside the parentheses:
\( (5x^3 + 4x^2) - (6x^2 - 2x - 9) = 5x^3 + 4x^2 - 6x^2 + 2x + 9 \)

Step2: Combine like terms

• For the \( x^2 \) terms: \( 4x^2 - 6x^2 = -2x^2 \)
• The \( x^3 \) term remains \( 5x^3 \), and the \( x \) term is \( +2x \), and the constant term is \( +9 \).

Putting it all together: \( 5x^3 - 2x^2 + 2x + 9 \)

Answer:

\( 5x^3 - 2x^2 + 2x + 9 \) (the fourth option: \( 5x^3 - 2x^2 + 2x + 9 \))