Problem 139 of 7
Verify the rational-expression rewrite: (x^3 + 3x^2 + 5x + 7) / (x^2 + 1) = x + 3 + (4x + 4)/(x^2 + 1).
Using a hint is okay. It just tells the trainer to give you a little more review.
Hidden until you reveal it.
multiply back and add remainder.
Hidden until you reveal it.
Verify by multiplying divisor by quotient and adding remainder.
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Your answer is equivalent to the expected form.
Walkthrough
Full solution stays hidden until you ask for it.
1. Identify divisor, quotient, and remainder.
2. Compute divisor times quotient plus remainder.
3. Compare with original numerator.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Checking by plugging one value only when algebraic verification is required.