Use the remainder theorem and the factor theorem to determine whether (c + 5) is a factor of (c4 + 7c3 + 6c2 − 18c + 10) A. The remainder isn't 0 and, therefore, (c + 5) is a factor of (c4 + 7c3 + 6c2 − 18c + 10) B. The remainder is 0 and, therefore, (c + 5) isn't a factor of (c4 + 7c3 + 6c2 − 18c + 10) C. The remainder is 0 and, therefore, (c + 5) is a factor of (c4 + 7c3 + 6c2 − 18c + 10) D. The remainder isn't 0 and, therefore, (c + 5) isn't a factor of (c4 + 7c3 + 6c2 − 18c + 10)

Question

Answer:

C. Use remainder theorem: If we divide a polynomial f(x) by (x-c) the remainder equals f(c). c=-5 in our case, so the remainder is f(-5). Plug in c=-5 into c4 + 7c3 + 6c2 − 18c + 10, f(-5)=0. Since the remainder is 0, (c+5) is a factor of the polynomial.

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