# SOLUTION: Im lost! Solve the problem. Find k such that f(x) = x4 + kx3 + 2 has the factor x + 1.

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 Click here to see ALL problems on Functions Question 362440: Im lost! Solve the problem. Find k such that f(x) = x4 + kx3 + 2 has the factor x + 1. Answer by CharlesG2(828)   (Show Source): You can put this solution on YOUR website!"Im lost! Solve the problem. Find k such that f(x) = x4 + kx3 + 2 has the factor x + 1." am sure this problem is f(x) = x^4 + kx^3 + 2, and we need to find k so that x + 1 is a factor divide: x^3 + (k - 1)x^2 - x + 1 x + 1 --> x^4 + kx^3 + 2 x^4 + x^3 (k - 1)x^3 + 2 (k - 1)x^3 + x^2 - x^2 + 2 - x^2 - x x + 2 x + 1 1 x^3 + (k - 1)x^2 - x + 1 + 1/(x + 1) was result of division (x^3 + (k - 1)x^2 - x + 1 + 1/(x + 1))(x + 1) x^3(x + 1) + (k - 1)(x + 1)x^2 - x(x + 1) + x + 1 + 1 x^4 + x^3 + (k - 1)(x^3 + x^2) - x^2 - x + x + 2 x^4 + x^3 + kx^3 + kx^2 - x^3 - x^2 - x^2 + 2 x^4 + kx^3 + kx^2 - 2x^2 + 2 x^4 + kx^3 + (k - 2)x^2 + 2 set k - 2 = 0 k = 2 to get x^4 + 2x^3 + 2 check: x^3 + x^2 - x + 1 x + 1 --> x^4 + 2x^3 + 2 x^4 + x^3 x^3 + 2 x^3 + x^2 2 - x^2 -x^2 - x 2 + x x + 1 1