Question

what is the sum of the polynomials?
(-x² + 9) + (-3x² - 11x + 4)
options:
-4x² - 2x + 4
-4x² - 11x + 13
2x² + 20x + 4
2x² + 11x + 5

Explanation:

Step1: Distribute the addition

We have \((-x^2 + 9) + (-3x^2 - 11x + 4)\). Remove the parentheses: \(-x^2 + 9 - 3x^2 - 11x + 4\).

Step2: Combine like terms for \(x^2\) terms

Combine \(-x^2\) and \(-3x^2\): \(-x^2 - 3x^2 = -4x^2\).

Step3: Combine like terms for \(x\) terms

There's only \(-11x\), so it remains \(-11x\).

Step4: Combine constant terms

Combine \(9\) and \(4\): \(9 + 4 = 13\).

Step5: Write the combined polynomial

Putting it all together: \(-4x^2 - 11x + 13\).

Answer:

\(-4x^2 - 11x + 13\) (corresponding to the second option: \(-4x^2 - 11x + 13\))