Find solutions to your problems with the help of IDNLearn.com's knowledgeable users. Our platform provides detailed and accurate responses from experts, helping you navigate any topic with confidence.

What is the sum of the polynomials?

[tex]\[
\left(-x^2+9\right)+\left(-3x^2-11x+4\right)
\][/tex]

A. [tex]\(-4x^2-2x+4\)[/tex]

B. [tex]\(-4x^2-11x+13\)[/tex]

C. [tex]\(2x^2+20x+4\)[/tex]

D. [tex]\(2x^2+11x+5\)[/tex]


Sagot :

Let's find the sum of the polynomials [tex]\(-x^2 + 9\)[/tex] and [tex]\(-3x^2 - 11x + 4\)[/tex].

1. Combine the [tex]\(x^2\)[/tex] terms:
- The first polynomial [tex]\(-x^2 + 9\)[/tex] has a term [tex]\(-x^2\)[/tex].
- The second polynomial [tex]\(-3x^2 - 11x + 4\)[/tex] has a term [tex]\(-3x^2\)[/tex].

Adding these terms together:
[tex]\[ -x^2 + (-3x^2) = -4x^2 \][/tex]

2. Combine the [tex]\(x\)[/tex] terms:
- The first polynomial [tex]\(-x^2 + 9\)[/tex] has no [tex]\(x\)[/tex] term (which is the same as having [tex]\(0 \cdot x\)[/tex]).
- The second polynomial [tex]\(-3x^2 - 11x + 4\)[/tex] has a term [tex]\(-11x\)[/tex].

Adding these terms together:
[tex]\[ 0x + (-11x) = -11x \][/tex]

3. Combine the constant terms:
- The first polynomial [tex]\(-x^2 + 9\)[/tex] has a constant term [tex]\(9\)[/tex].
- The second polynomial [tex]\(-3x^2 - 11x + 4\)[/tex] has a constant term [tex]\(4\)[/tex].

Adding these terms together:
[tex]\[ 9 + 4 = 13 \][/tex]

So, the sum of the polynomials [tex]\(-x^2 + 9\)[/tex] and [tex]\(-3x^2 - 11x + 4\)[/tex] is:
[tex]\[ -4x^2 - 11x + 13 \][/tex]

The correct answer is:
[tex]\[ -4 x^2 - 11 x + 13 \][/tex]