Let's expand the given expression step by step to write it as a polynomial in standard form:
Original expression:
[tex]\[
(x + 2)\left(3x^2 + 5x + 10\right)
\][/tex]
Step 1: Distribute [tex]\(x\)[/tex] across each term inside the parentheses:
[tex]\[
x \cdot \left(3x^2 + 5x + 10\right) = 3x^3 + 5x^2 + 10x
\][/tex]
Step 2: Distribute [tex]\(2\)[/tex] across each term inside the parentheses:
[tex]\[
2 \cdot \left(3x^2 + 5x + 10\right) = 6x^2 + 10x + 20
\][/tex]
Step 3: Add the results from Step 1 and Step 2 together:
[tex]\[
3x^3 + 5x^2 + 10x + 6x^2 + 10x + 20
\][/tex]
Step 4: Combine like terms:
[tex]\[
3x^3 + (5x^2 + 6x^2) + (10x + 10x) + 20
\][/tex]
[tex]\[
3x^3 + 11x^2 + 20x + 20
\][/tex]
So, the expanded polynomial in standard form is:
[tex]\[
3x^3 + 11x^2 + 20x + 20
\][/tex]
