Question

A student uses the division shown to divide –3x4 + 15x3 – x + 5 by x – 5, and concludes that x – 5 is not a factor of the polynomial. es002-1.jpg Describe two errors the student made. Is x – 5 a factor? Explain.

Answer 1

The student used k = –5 instead of k = 5. And the student did not use a placeholder zero for the x2 term. Also, x – 5 is a factor because there is no remainder when the division is performed correctly.

Answer 2

Recognize that the student used k = –5 instead of k = 5.Recognize that the student did not use a placeholder zero for the x2 term.Conclude that x – 5 is a factor because there is no remainder when the division is performed correctly.