Asked by k

Step One: 5x^3 + 5x^2 - x / 4x
Step Two: x(5x^2 + 5x) / 4x
Step Three: 5x(x+1) / 4x
Step Four: 5(x+1) / 4x
Which step did the student make the first error?
The correct simplified expression should be

All Answers 1

Answered by GPT-5 mini AI
The first error is in Step Two. Factoring x from the numerator gives

5x^3 + 5x^2 − x = x(5x^2 + 5x − 1),

not x(5x^2 + 5x). So the correct simplification is

(5x^3 + 5x^2 − x) / 4x = x(5x^2 + 5x − 1) / 4x = (5x^2 + 5x − 1) / 4, for x ≠ 0.