Question

Add. Express your answer as a polynomial in standard form. (1 point)
(6x3−8x2+3x)+(10x2+9x+11)=
(
6
𝑥
3
−
8
𝑥
2
+
3
𝑥
)
+
(
10
𝑥
2
+
9
𝑥
+
11
)
=

Answer 1

To add the two polynomials \((6x^3 - 8x^2 + 3x)\) and \((10x^2 + 9x + 11)\), we'll combine like terms.

1. **Identify the terms from both polynomials**:
- From \(6x^3 - 8x^2 + 3x\):
- \(6x^3\) (cubic term)
- \(-8x^2\) (quadratic term)
- \(3x\) (linear term)
- From \(10x^2 + 9x + 11\):
- \(10x^2\) (quadratic term)
- \(9x\) (linear term)
- \(11\) (constant term)

2. **Combine like terms**:
- Cubic terms: \(6x^3\)
- Quadratic terms: \(-8x^2 + 10x^2 = 2x^2\)
- Linear terms: \(3x + 9x = 12x\)
- Constant terms: \(11\)

3. **Write the result as a polynomial in standard form**:
\[
6x^3 + 2x^2 + 12x + 11
\]

Thus, the final answer is:
\[
\boxed{6x^3 + 2x^2 + 12x + 11}
\]