if x-3 is a factor of x^4-3x^3+kx+3, what is the value of k?

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if x-3 is a factor of x^4-3x^3+kx+3, what is the value of k?

2007-10-29 14:15:20 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

2 answers

f(x) = x^4 - 3x^3 + kx + 3

If (x-3) is a factor, by the Factor Theorem, f(3) = 0

f(3) = 3^4 - 3*3^3 + 3k + 3
= 81 - 81 + 3k + 3
= 3k + 3

3k + 3 = 0
3k = -3
k = -1

2007-10-29 14:20:40 · answer #1 · answered by gudspeling 7 · 0⤊ 0⤋

Using synthetic division:-
3|1____-3____k____3
" |_____3____0____3k
" |1____0____k___3 + 3k

R = 3 + 3k = 0
3k = - 3
k = - 1

2007-11-02 12:04:36 · answer #2 · answered by Como 7 · 0⤊ 0⤋