IDNLearn.com: Where curiosity meets clarity and questions find their answers. Our platform offers reliable and comprehensive answers to help you make informed decisions quickly and easily.

What is the sum of the polynomials?

[tex]\[ \left(6x + 7 + x^2\right) + \left(2x^2 - 3\right) \][/tex]

A. [tex]\(-x^2 + 6x + 4\)[/tex]

B. [tex]\(3x^2 + 6x + 4\)[/tex]

C. [tex]\(9x + 4\)[/tex]

D. [tex]\(9x^2 + 4\)[/tex]


Sagot :

To find the sum of the polynomials, we need to add the coefficients of corresponding powers of [tex]\(x\)[/tex]. We are given the polynomials:

[tex]\[ 6x + 7 + x^2 \][/tex]
and
[tex]\[ 2x^2 - 3 \][/tex]

Let's rewrite these polynomials in a standard form from the highest degree to the constant term to clearly see the coefficients:

[tex]\[ x^2 + 6x + 7 \][/tex]
and
[tex]\[ 2x^2 - 3 + 0x \][/tex]

Now we align the polynomials by their degrees:

[tex]\[ \begin{array}{r} 1x^2 + 6x + 7 \\ + 2x^2 + 0x - 3 \\ \hline \end{array} \][/tex]

Next, we add the coefficients of the corresponding powers of [tex]\(x\)[/tex]:

- For [tex]\(x^2\)[/tex] : [tex]\(1 + 2 = 3\)[/tex]
- For [tex]\(x\)[/tex] : [tex]\(6 + 0 = 6\)[/tex]
- For the constant term: [tex]\(7 - 3 = 4\)[/tex]

Thus, the resulting polynomial after adding is:

[tex]\[ 3x^2 + 6x + 4 \][/tex]

So, the sum of the given polynomials is:

[tex]\[ 3x^2 + 6x + 4 \][/tex]

The correct answer is:
[tex]\[ 3x^2 + 6x + 4 \][/tex]