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

Since the polynomial function at x = 5 is zero, hence x - 5 is a factor of the polynomial function.

• Given the polynomial function expressed as $-3x^4 + 15x^3 -x + 5$, we need to determine whether x - 5 is a factor or not.

To do that, we need to first equate x - 5 to zero and calculate the value of x"

• x - 5 = 0
• x = 0 + 5
• x = 5

Check if P(5) = 0;

• P(x)= -3x^4 + 15x^3 -x + 5
• P(5)= -3(5)^4 + 15(5)^3 -5 + 5
• P(5) = -1875 + 1875 - 5 + 5
• P(5) = 0

Since the polynomial function at x = 5 is zero, hence x - 5 is a factor of the polynomial.

Learn more on remainder theorem here: https://brainly.com/question/13328536