If (x - 5) is the HCF of x^2 - x - p and x^2 - qx - 10, then what is the value of (p + q) ?

Explanation

Since x-5 is a factor, substituting x=5 into both polynomials yields 0. For the first, 25-5-p=0 \implies p=20. For the second, 25-5q-10=0 \implies q=3. Therefore, p+q = 23.

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