Question

Simplify 2x squared- 7X - 4 / x - 4 write your answer in standard form

Answer 1

To simplify the expression \(\frac{2x^2 - 7x - 4}{x - 4}\), we will perform polynomial long division.

1. **Set up the division**:
We want to divide \(2x^2 - 7x - 4\) by \(x - 4\).

2. **First term**:
Divide the leading term of the dividend by the leading term of the divisor:
\[
\frac{2x^2}{x} = 2x
\]
This means \(2x\) will be the first term of the quotient.

3. **Multiply and subtract**:
Multiply \(2x\) by the entire divisor \(x - 4\):
\[
2x(x - 4) = 2x^2 - 8x
\]
Now, subtract this result from the original polynomial:
\[
(2x^2 - 7x - 4) - (2x^2 - 8x) = -7x + 8x - 4 = x - 4
\]

4. **Next term**:
Now divide the new polynomial \(x - 4\) by \(x - 4\):
\[
\frac{x}{x} = 1
\]
So the next term of the quotient is \(1\).

5. **Multiply and subtract**:
Multiply \(1\) by \(x - 4\):
\[
1(x - 4) = x - 4
\]
Now subtract this from the current remainder:
\[
(x - 4) - (x - 4) = 0
\]

Now that we have a remainder of \(0\), the division is complete.

6. **Putting it all together**:
The quotient of the division is:
\[
2x + 1
\]

Therefore, the simplified form of \(\frac{2x^2 - 7x - 4}{x - 4}\) in standard form is:
\[
\boxed{2x + 1}
\]