Question

which polynomial represents the sum below?
$\

$$\begin{array}{r}\\ 9x^{2}+x+2 \\\\\\ +\\ 3x^{4}+2x+2 \\\\\\ \\hline\\end{array}$$

$
\\(\bigcirc\\) a. \\(3x^{4}+9x+4\\)
\\(\bigcirc\\) b. \\(3x^{4}+9x^{2}+3x+4\\)
\\(\bigcirc\\) c. \\(12x^{6}+9x+4\\)
\\(\bigcirc\\) d. \\(3x^{6}+9x^{2}+3x+4\\)

Explanation:

Step1: Combine like terms for \(x^4\)

The term with \(x^4\) is \(3x^4\) (only in the second polynomial), so we keep it as is: \(3x^4\)

Step2: Combine like terms for \(x^2\)

The term with \(x^2\) is \(9x^2\) (only in the first polynomial), so we keep it as is: \(9x^2\)

Step3: Combine like terms for \(x\)

The terms with \(x\) are \(x\) (from first polynomial) and \(2x\) (from second polynomial). Adding them: \(x + 2x = 3x\)

Step4: Combine like terms for constants

The constant terms are \(2\) (from first polynomial) and \(2\) (from second polynomial). Adding them: \(2 + 2 = 4\)

Step5: Combine all terms

Putting it all together: \(3x^4 + 9x^2 + 3x + 4\)

Answer:

B. \(3x^4 + 9x^2 + 3x + 4\)