Question

When the polynomial mx^3-3x^2+nx+2 is divided by x+3, the reminder is -1. When it is divided by x-2, the reminder is -4. What are the values of m and n?

Answer 1

let p(x) = mx^3-3x^2+nx+2

Answer 2

according to the remainder theorem, if you divide p(x) by x-k, then p(k) is the remainder

Answer 3

when "mx^3-3x^2+nx+2 is divided by x+3, the reminder is -1"

so p(-3) = -1 because x+3 is in the form x-(-3) and k = -3

Answer 4

so plug x = -3 into mx^3-3x^2+nx+2 and set it equal to -1

mx^3-3x^2+nx+2

m(-3)^3-3(-3)^2+n(-3)+2 = -1

-27m - 27 - 3n + 2 = -1

that's one equation you can work with to solve for m and n

Answer 5

to find the other, plug x = 2 into mx^3-3x^2+nx+2 and set it equal to -4