Question

Which expression is equivalent to (3x^2+ 4x -7)(x - 2)?

Answer 1

To find the expression equivalent to \((3x^2 + 4x - 7)(x - 2)\), we can use the distributive property (also known as the FOIL method for binomials).

We will distribute each term in the first polynomial, \(3x^2 + 4x - 7\), by each term in the second polynomial, \(x - 2\):

1. \(3x^2 \cdot x = 3x^3\)
2. \(3x^2 \cdot (-2) = -6x^2\)
3. \(4x \cdot x = 4x^2\)
4. \(4x \cdot (-2) = -8x\)
5. \(-7 \cdot x = -7x\)
6. \(-7 \cdot (-2) = 14\)

Now, we add all these results together:

\[
3x^3 - 6x^2 + 4x^2 - 8x - 7x + 14
\]

Next, we combine like terms:

- For \(x^2\): \(-6x^2 + 4x^2 = -2x^2\)
- For \(x\): \(-8x - 7x = -15x\)

Putting it all together, we have:

\[
3x^3 - 2x^2 - 15x + 14
\]

Thus, the expression equivalent to \((3x^2 + 4x - 7)(x - 2)\) is:

\[
\boxed{3x^3 - 2x^2 - 15x + 14}
\]