Question

Find the product of (2x^2+ x +3) (x − 2)

Answer 1

To find the product of the two polynomials \( (2x^2 + x + 3)(x - 2) \), we can use the distributive property (also known as the FOIL method for binomials). We'll multiply each term in the first polynomial by each term in the second polynomial.

1. Multiply \( 2x^2 \) by \( x \):
\[
2x^2 \cdot x = 2x^3
\]

2. Multiply \( 2x^2 \) by \( -2 \):
\[
2x^2 \cdot (-2) = -4x^2
\]

3. Multiply \( x \) by \( x \):
\[
x \cdot x = x^2
\]

4. Multiply \( x \) by \( -2 \):
\[
x \cdot (-2) = -2x
\]

5. Multiply \( 3 \) by \( x \):
\[
3 \cdot x = 3x
\]

6. Multiply \( 3 \) by \( -2 \):
\[
3 \cdot (-2) = -6
\]

Now, we combine all of these results:
\[
2x^3 - 4x^2 + x^2 - 2x + 3x - 6
\]

Next, we combine like terms:
- The \( x^2 \) terms: \( -4x^2 + x^2 = -3x^2 \)
- The \( x \) terms: \( -2x + 3x = x \)

Putting it all together, we have:
\[
2x^3 - 3x^2 + x - 6
\]

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