College

Simplify the polynomial by combining like terms:

[tex]\[ 3x^9 + 11x^4 + 13x^9 + 3x^9 - 1x^4 \][/tex]

Options:
A. [tex]\[ 29x^9 + 29x^4 \][/tex]
B. [tex]\[ 19x^9 + 10x^4 \][/tex]
C. [tex]\[ 29x^9 \][/tex]
D. [tex]\[ 3x^9 + 11x^4 + 13x^9 + 3x^9 - 1x^4 \][/tex]

Answer :

Sure! Let's simplify the polynomial by combining like terms step-by-step.

We start with the polynomial:

[tex]\[ 3x^9 + 11x^4 + 13x^9 + 3x^9 - 1x^4 \][/tex]

Step 1: Identify like terms

- The terms with [tex]\(x^9\)[/tex] are: [tex]\(3x^9\)[/tex], [tex]\(13x^9\)[/tex], and [tex]\(3x^9\)[/tex].
- The terms with [tex]\(x^4\)[/tex] are: [tex]\(11x^4\)[/tex] and [tex]\(-1x^4\)[/tex].

Step 2: Combine the like terms

- For terms with [tex]\(x^9\)[/tex]: Combine [tex]\(3x^9 + 13x^9 + 3x^9\)[/tex].
[tex]\[
(3 + 13 + 3)x^9 = 19x^9
\][/tex]

- For terms with [tex]\(x^4\)[/tex]: Combine [tex]\(11x^4 - 1x^4\)[/tex].
[tex]\[
(11 - 1)x^4 = 10x^4
\][/tex]

Step 3: Write the simplified polynomial

By combining the like terms, we get:
[tex]\[
19x^9 + 10x^4
\][/tex]

So, the simplified polynomial is [tex]\(19x^9 + 10x^4\)[/tex].

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