Question

add.
$(-x^3 + 26x^2 - 7x - 13) + (6x^4 - x^3 + 8x + 27)$
express the answer in standard form.
enter your answer in the box.

Explanation:

Step1: Remove parentheses

To add the two polynomials, we first remove the parentheses:
$$(-x^3 + 26x^2 - 7x - 13) + (6x^4 - x^3 + 8x + 27)= -x^3 + 26x^2 - 7x - 13 + 6x^4 - x^3 + 8x + 27$$

Step2: Combine like terms

• For the \(x^4\) term: There is only \(6x^4\).
• For the \(x^3\) terms: \(-x^3 - x^3 = -2x^3\)
• For the \(x^2\) term: There is only \(26x^2\).
• For the \(x\) terms: \(-7x + 8x = x\)
• For the constant terms: \(-13 + 27 = 14\)

Now, we write the polynomial in standard form (descending powers of \(x\)):
$$6x^4 - 2x^3 + 26x^2 + x + 14$$

Answer:

\(6x^4 - 2x^3 + 26x^2 + x + 14\)