Question

Find the difference between thetwopolynomials,showingallworkbelow(9x2+17x+13)−(2x2+12x+11)

Answer 1

To find the difference between the two polynomials \((9x^2 + 17x + 13)\) and \((2x^2 + 12x + 11)\), we can follow these steps:

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

2. **Distribute the negative sign across the second polynomial**:
\[
= 9x^2 + 17x + 13 - 2x^2 - 12x - 11
\]

3. **Combine like terms**:
- Start with the \(x^2\) terms:
\[
9x^2 - 2x^2 = (9 - 2)x^2 = 7x^2
\]
- Then the \(x\) terms:
\[
17x - 12x = (17 - 12)x = 5x
\]
- Lastly, the constant terms:
\[
13 - 11 = 2
\]

4. **Put it all together**:
The combined result of the polynomials is:
\[
7x^2 + 5x + 2
\]

So, the difference between the two polynomials is:
\[
\boxed{7x^2 + 5x + 2}
\]