If (x - 1) and (x + 1) both leave remainder 0 when dividing p(x) = x^3 + ax^2 + bx + c, and p(0) = -1, find the value of a. (Note: remainder 0 means the value of p at that point is 0.)

Question

Accepted Answer

1. p(0) = c = -1. p(1) = 1 + a + b + c = 0 so a + b = 0. p(-1) = -1 + a - b + c = 0 so a - b = 2. Adding: 2a = 2, a = 1.

If $(x - 1)$ and $(x + 1)$ both leave remainder 0 when dividing $p (x) = x^{3} + a x^{2} + b x + c$ , and $p (0) = - 1$ , find the value of a.
(Note: remainder 0 means the value of $p$ at that point is 0.)

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 9 Remainder Theorem practice

If (x−1) and (x+1) both leave remainder 0 when dividing p(x)=x3+ax2+bx+c, and p(0)=−1, find the value of a.(Note: remainder 0 means the value of p at that point is 0.)

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 9 Remainder Theorem practice

If $(x - 1)$ and $(x + 1)$ both leave remainder 0 when dividing $p (x) = x^{3} + a x^{2} + b x + c$ , and $p (0) = - 1$ , find the value of a.
(Note: remainder 0 means the value of $p$ at that point is 0.)