To find the sum of the given polynomials, we need to add the corresponding coefficients of each term. Let's break down the process step-by-step.
The polynomials given are:
[tex]\[ P(x) = x^2 - x + 7 \][/tex]
[tex]\[ Q(x) = 9x^2 + 6 \][/tex]
1. Identify the coefficients for each term:
- For [tex]\(P(x) = x^2 - x + 7\)[/tex]:
- Coefficient of [tex]\(x^2\)[/tex]: [tex]\(1\)[/tex]
- Coefficient of [tex]\(x\)[/tex]: [tex]\(-1\)[/tex]
- Constant term: [tex]\(7\)[/tex]
- For [tex]\(Q(x) = 9x^2 + 6\)[/tex]:
- Coefficient of [tex]\(x^2\)[/tex]: [tex]\(9\)[/tex]
- Coefficient of [tex]\(x\)[/tex]: [tex]\(0\)[/tex]
- Constant term: [tex]\(6\)[/tex]
2. Add the coefficients of the [tex]\(x^2\)[/tex] terms:
[tex]\[ 1\text{ (from } x^2\text{ in } P(x)) + 9\text{ (from } x^2\text{ in } Q(x)) = 10 \][/tex]
So the coefficient of [tex]\(x^2\)[/tex] in the sum is [tex]\(10\)[/tex].
3. Add the coefficients of the [tex]\(x\)[/tex] terms:
[tex]\[ -1\text{ (from } x\text{ in } P(x)) + 0\text{ (from } x\text{ in } Q(x)) = -1 \][/tex]
So the coefficient of [tex]\(x\)[/tex] in the sum is [tex]\(-1\)[/tex].
4. Add the constant terms:
[tex]\[ 7\text{ (from constant term in } P(x)) + 6\text{ (from constant term in } Q(x)) = 13 \][/tex]
So the constant term in the sum is [tex]\(13\)[/tex].
5. Form the resulting polynomial:
By combining all these terms, the resulting polynomial is:
[tex]\[ 10x^2 - x + 13 \][/tex]
Therefore, the sum of the polynomials is:
[tex]\[ \boxed{B. \; 10x^2 - x + 13} \][/tex]
