Question

question
find the sum of $-7x^2 - 1$ and $x^2 - x - 5$.

answer attempt 1 out of 2

Explanation:

Step1: Write the sum expression

To find the sum of \(-7x^2 - 1\) and \(x^2 - x - 5\), we write the expression as \((-7x^2 - 1)+(x^2 - x - 5)\).

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

The \(x^2\) terms are \(-7x^2\) and \(x^2\). Combining them: \(-7x^2+x^2 = (-7 + 1)x^2=-6x^2\).

Step3: Identify and handle the \(x\) term

There is only one \(x\) term, which is \(-x\) (from the second polynomial), so we keep it as is.

Step4: Combine the constant terms

The constant terms are \(-1\) and \(-5\). Combining them: \(-1+(-5)=-6\).

Step5: Combine all the results

Putting together the combined like terms, we get \(-6x^2 - x - 6\).

Answer:

\(-6x^2 - x - 6\)