Question

Find the product of (2x^2+ x +3)(x−2)

Answer 1

To find the product of \((2x^2 + x + 3)(x - 2)\), we can use the distributive property (also known as the FOIL method).

1. Distribute \(x\) to each term in the polynomial \(2x^2 + x + 3\):
\[
x \cdot (2x^2) + x \cdot (x) + x \cdot (3) = 2x^3 + x^2 + 3x
\]

2. Distribute \(-2\) to each term in the polynomial \(2x^2 + x + 3\):
\[
-2 \cdot (2x^2) + (-2) \cdot (x) + (-2) \cdot (3) = -4x^2 - 2x - 6
\]

3. Now combine all the terms from the two distributions:
\[
2x^3 + x^2 + 3x - 4x^2 - 2x - 6
\]

4. Combine like terms:
- The \(x^2\) terms: \(x^2 - 4x^2 = -3x^2\)
- The \(x\) terms: \(3x - 2x = 1x\)
- The constant: \(-6\)

So, we get:
\[
2x^3 - 3x^2 + x - 6
\]

Therefore, the product of \((2x^2 + x + 3)(x - 2)\) is:
\[
\boxed{2x^3 - 3x^2 + x - 6}
\]