Add. Express your answer as a polynomial in standard form. (1 point)

Question

(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: \[ \boxed{6x^3 + 2x^2 + 12x + 11} \]