Consider the following function: p(x) = x^3 -2x +13x+ k. The remainder of the division of p(x) by (x+1) is -10. What is the remainder of the division of p(x) by (x-1)?

Answer 1

k=-22

just replace x by 1 and p(1) = 1-2+13+k = -10, so k=-22 (I'm assuming you left out a 2 as the exponent for x in the 2nd term -2x)

divide x-1 into x^3-2x^2 +13x -22 and the remainder is the same as plugging 1 in the place of x to get

1-2+13-22 = -10

but if you really didn't leave out that 2 exponent, then you're dividing x-1 into x^3+11x+k

plug 1 in, and you get 1+11+k=-10 and k=-22

divide x-1 into x^3+11x-22 gives

remainder of 1+11-22 = -10

or do long or synthetic division, and you get the same results