Question

Simplify the polynomial expression 7x2+2x−97x+9+(x+2)(x−3) .

Answer 1

To simplify the polynomial expression \( 7x^2 + 2x - 97x + 9 + (x+2)(x-3) \), we can follow these steps:

1. **Combine like terms** in the polynomial:

The terms \( 2x \) and \( -97x \) can be combined:
\[
2x - 97x = -95x
\]

Substituting this back into the polynomial gives us:
\[
7x^2 - 95x + 9
\]

2. **Expand the product** \((x+2)(x-3)\):

Using the distributive property (FOIL method):
\[
(x+2)(x-3) = x^2 - 3x + 2x - 6 = x^2 - x - 6
\]

3. **Combine the expanded expression** with the earlier polynomial:
\[
7x^2 - 95x + 9 + (x^2 - x - 6)
\]

Combine the terms:
- For the \(x^2\) terms:
\[
7x^2 + x^2 = 8x^2
\]
- For the \(x\) terms:
\[
-95x - x = -96x
\]
- For the constant terms:
\[
9 - 6 = 3
\]

4. **Write the final simplified polynomial**:
\[
8x^2 - 96x + 3
\]

Thus, the simplified form of the expression is:
\[
\boxed{8x^2 - 96x + 3}
\]