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

Mathematics

Maia Travis

15 December, 16:36

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)

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Answers (1)

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Marilyn Johns · Answer 1

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.