Answer :
Sure! Let's add the two polynomials step by step.
We're given two polynomials:
1. [tex]\(-6x^4 - 2x^3 - 9x\)[/tex]
2. [tex]\(-7x^4 - 9x^3 - 10\)[/tex]
To add these polynomials, we follow these steps:
1. Align the Like Terms: Write the terms of each polynomial under one another, matching the terms with the same powers of [tex]\(x\)[/tex]:
[tex]\[
\begin{align*}
-6x^4 & - 2x^3 + 0x^2 - 9x + 0 \\
-7x^4 & - 9x^3 + 0x^2 + 0x - 10 \\
\end{align*}
\][/tex]
2. Add the Coefficients of Like Terms: Add the coefficients of the terms with the same power:
[tex]\[
\begin{align*}
(-6x^4) + (-7x^4) &= -13x^4 \\
(-2x^3) + (-9x^3) &= -11x^3 \\
(0x^2) + (0x^2) &= 0x^2 \\
(-9x) + (0x) &= -9x \\
(0) + (-10) &= -10 \\
\end{align*}
\][/tex]
3. Write the Resulting Polynomial: Combine all the terms we found:
[tex]\[
-13x^4 - 11x^3 + 0x^2 - 9x - 10
\][/tex]
So, the sum of the two polynomials is [tex]\(-13x^4 - 11x^3 - 9x - 10\)[/tex].
We're given two polynomials:
1. [tex]\(-6x^4 - 2x^3 - 9x\)[/tex]
2. [tex]\(-7x^4 - 9x^3 - 10\)[/tex]
To add these polynomials, we follow these steps:
1. Align the Like Terms: Write the terms of each polynomial under one another, matching the terms with the same powers of [tex]\(x\)[/tex]:
[tex]\[
\begin{align*}
-6x^4 & - 2x^3 + 0x^2 - 9x + 0 \\
-7x^4 & - 9x^3 + 0x^2 + 0x - 10 \\
\end{align*}
\][/tex]
2. Add the Coefficients of Like Terms: Add the coefficients of the terms with the same power:
[tex]\[
\begin{align*}
(-6x^4) + (-7x^4) &= -13x^4 \\
(-2x^3) + (-9x^3) &= -11x^3 \\
(0x^2) + (0x^2) &= 0x^2 \\
(-9x) + (0x) &= -9x \\
(0) + (-10) &= -10 \\
\end{align*}
\][/tex]
3. Write the Resulting Polynomial: Combine all the terms we found:
[tex]\[
-13x^4 - 11x^3 + 0x^2 - 9x - 10
\][/tex]
So, the sum of the two polynomials is [tex]\(-13x^4 - 11x^3 - 9x - 10\)[/tex].
