# Math Help - remainder theorem 2

1. ## remainder theorem 2

i dont understand how to solve this equation so if anyone could help that would be greatly appreaciated

When kx^3 + px^2 -x + 3 is divided by x - 1, the remainder is 4. When kx^3 + px^2 -x + 3 is divided by x- 2, the remainder is 21. What are the values of k and p?

2. Originally Posted by flwer_13
i dont understand how to solve this equation so if anyone could help that would be greatly appreaciated

When kx^3 + px^2 -x + 3 is divided by x - 1, the remainder is 4. When kx^3 + px^2 -x + 3 is divided by x- 2, the remainder is 21. What are the values of k and p?
remainder theorem ...

If a polynomial P(x) is divided by (x − r), then the remainder of this division is the same as evaluating P(r).

so ...

$k(1)^3 + p(1)^2 - (1) + 3 = 4$

$k(2)^3 + p(2)^2 - (2) + 3 = 21$

solve the system for k and p