Answer to Question #224774 in Algebra for Kofy

Question

P(m)=X^3+mx2-x+12 when P(m) is divided by (x-1) the remainder is r. When P(m) is divided by (x-4) the remainder is 8r. Determine the values of m and r

Answer 1

$$(1)^3+m(1)^2-1+12=r$$

$$(4)^3+m(4)^2-4+12=8r$$

$$m=r-12$$

$$2m=r-9$$

$$m=3$$

$$r=15$$