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. Describe two errors the student made. Is x – 5 a factor? Explain.

Answer:

The student made two errors: they used k = -5 instead of k = 5, and they omitted the placeholder 0 for the missing x^2 term. Using k = 5 with coefficients -3, 15, 0, -1, 5 gives a remainder of 0, so x - 5 is a factor.