Certainly! To add the polynomials [tex]\( (8x + 5) \)[/tex] and [tex]\( (-3x - 20) \)[/tex], follow these steps:
1. Identify the coefficients of like terms:
- The coefficients of [tex]\( x \)[/tex] in the polynomials are [tex]\( 8 \)[/tex] from [tex]\( 8x \)[/tex] and [tex]\( -3 \)[/tex] from [tex]\( -3x \)[/tex].
- The constant terms are [tex]\( 5 \)[/tex] and [tex]\( -20 \)[/tex].
2. Add the coefficients of like terms:
- For the terms with [tex]\( x \)[/tex]:
[tex]\[
8 + (-3) = 5
\][/tex]
- For the constant terms:
[tex]\[
5 + (-20) = -15
\][/tex]
3. Combine the results:
- The result for the [tex]\( x \)[/tex] term is [tex]\( 5x \)[/tex].
- The result for the constant term is [tex]\( -15 \)[/tex].
So, the sum of the polynomials [tex]\( (8x + 5) \)[/tex] and [tex]\( (-3x - 20) \)[/tex] is:
[tex]\[
5x - 15
\][/tex]
Thus, the final answer is:
[tex]\[
5x - 15
\][/tex]
