Answer :
Answer:
The quotient when dividing P(x) = x^3 + x^2 - 36 by the binomial x - 3 is x^2 + 4x + 12.
Step-by-step explanation:
To find the quotient when dividing P(x) = x^3 + x^2 - 36 by the binomial x - 3, we use the long division method.
Step 1: Divide the first term of the polynomial (x^3) by the first term of the binomial (x).
Step 2: Multiply the quotient obtained in Step 1 (x^2) by the binomial (x - 3) and subtract the result from the polynomial.
Step 3: Repeat Steps 1 and 2 with the new polynomial obtained in Step 2.
Step 4: Continue the process until all terms have been divided.
Step 5: The quotient is the sum of the quotients obtained in each step.
Using the long division method, we find that the quotient when dividing P(x) by x - 3 is x^2 + 4x + 12.
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