Which of the following correctly simplifies (9x2+17x+13)−(2x2+12x+11)

Question

(
9
𝑥
2
+
17
𝑥
+
13
)
−
(
2
𝑥
2
+
12
𝑥
+
11
)
?(1 point)
Responses

7x2+29x+24
7
𝑥
2
+
29
𝑥
+
24
7 x squared plus 29 x plus 24

12x2+2
12
𝑥
2
+
2
12 x squared plus 2

7x2+5x+2
7
𝑥
2
+
5
𝑥
+
2
7 x squared plus 5 x plus 2

9x2+17x+13−2x2−12x−11

Answer 1

To simplify the expression \((9x^2 + 17x + 13) - (2x^2 + 12x + 11)\), we will first distribute the negative sign to the second polynomial.

1. Write the expression: \[ (9x^2 + 17x + 13) - (2x^2 + 12x + 11) \]

2. Distribute the negative sign: \[ 9x^2 + 17x + 13 - 2x^2 - 12x - 11 \]

3. Combine like terms:

   • For \(x^2\) terms: \[ 9x^2 - 2x^2 = 7x^2 \]
   • For \(x\) terms: \[ 17x - 12x = 5x \]
   • For constant terms: \[ 13 - 11 = 2 \]

4. Putting it all together: \[ 7x^2 + 5x + 2 \]

So the correct simplification is: \[ \boxed{7x^2 + 5x + 2} \]