What is the sum of the polynomials?

[tex]\[
\begin{array}{r}
11x^2 - 5 \\
+ \quad x + 4 \\
\hline
\end{array}
\][/tex]

A. [tex]\(10x^2 - 9\)[/tex]

B. [tex]\(11x^2 - x - 9\)[/tex]

C. [tex]\(11x^2 + x - 1\)[/tex]

D. [tex]\(12x^2 - 1\)[/tex]



Answer :

Let's solve the problem step by step:

We are given two polynomials:
[tex]\[ P(x) = 11x^2 - 5 \][/tex]
[tex]\[ Q(x) = x + 4 \][/tex]

We want to find the sum of these polynomials, [tex]\( P(x) + Q(x) \)[/tex].

1. Identify the coefficients of each polynomial:

For [tex]\( P(x) = 11x^2 - 5 \)[/tex]:
- The coefficient of [tex]\( x^2 \)[/tex] is 11.
- The coefficient of [tex]\( x \)[/tex] is 0 (since there is no [tex]\( x \)[/tex] term).
- The constant term is -5.

For [tex]\( Q(x) = x + 4 \)[/tex]:
- The coefficient of [tex]\( x^2 \)[/tex] is 0 (since there is no [tex]\( x^2 \)[/tex] term).
- The coefficient of [tex]\( x \)[/tex] is 1.
- The constant term is 4.

2. Add the corresponding coefficients:

For [tex]\( x^2 \)[/tex] terms:
[tex]\( 11 + 0 = 11 \)[/tex]

For [tex]\( x \)[/tex] terms:
[tex]\( 0 + 1 = 1 \)[/tex]

For the constant terms:
[tex]\( -5 + 4 = -1 \)[/tex]

3. Write out the sum polynomial using the summed coefficients:

Combining these results, we get:
[tex]\[ P(x) + Q(x) = 11x^2 + x - 1 \][/tex]

So, the sum of the given polynomials is:
[tex]\[ 11x^2 + x - 1 \][/tex]

Thus, the option that corresponds to this polynomial is:
[tex]\[ \boxed{11x^2 + x - 1} \][/tex]