Question

The remainder when x^3−px^2+6x−p is divided by x−p is:

a) 6
b) p
c) p−6
d) p+6

Answer 1

The remainder when the polynomial x^3−px^2+6x−p is divided by x−p is p−6.

Step-by-step explanation:

To find the remainder when a polynomial is divided by a linear binomial of the form x - r, you can use the Remainder Theorem. According to the theorem, the remainder of the division of a polynomial f(x) by x - r is equal to f(r). Hence, to find the remainder when x^3 - px^2 + 6x - p is divided by x - p, we need to evaluate the polynomial at x = p, which gives p^3 - p(p^2) + 6p - p. This simplifies to p - 6.