Divide (x^5-32)/(x-2)

Problem

(x^5−32)/(x−2)

Solution

1. Identify the expression as a division of a binomial by a linear factor, which can be solved using synthetic division or the formula for the difference of nth powers.

2. Apply the formula for the difference of powers a^n−b^n=(a−b)*(a^(n−1)+a^(n−2)*b+a^(n−3)*b^2+⋯+b^(n−1))

3. Substitute a=x b=2 and n=5 into the formula.

4. Expand the resulting terms to find the quotient.

5. Simplify each term by calculating the powers of 2.

Final Answer

(x^5−32)/(x−2)=x^4+2*x^3+4*x^2+8*x+16

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