Question

Simplify 2x^2−7x−4/x−4 . Write your answer in standard form.(1 point)

Answer 1

To simplify the expression \(\frac{2x^2 - 7x - 4}{x - 4}\), we can start by factoring the numerator, \(2x^2 - 7x - 4\).

First, we'll try to factor the quadratic:

1. We need two numbers that multiply to \(2 \cdot (-4) = -8\) and add up to \(-7\). The numbers \(-8\) and \(1\) work because:
\[
-8 \times 1 = -8 \quad \text{and} \quad -8 + 1 = -7
\]

2. Rewrite the quadratic by splitting the middle term:
\[
2x^2 - 8x + x - 4
\]

3. Now, factor by grouping:
\[
(2x^2 - 8x) + (x - 4) = 2x(x - 4) + 1(x - 4)
\]

4. Factor out the common term \((x - 4)\):
\[
(2x + 1)(x - 4)
\]

Now, substitute back into the original expression:
\[
\frac{2x^2 - 7x - 4}{x - 4} = \frac{(2x + 1)(x - 4)}{x - 4}
\]

Assuming \(x \neq 4\) (to avoid division by zero), we can cancel the \((x - 4)\) terms:
\[
2x + 1
\]

Thus, the simplified form of the expression is:
\[
2x + 1
\]

In standard form, the answer is:
\[
\boxed{2x + 1}
\]