use synthetic division to find k given that x-2 is a factor of f(x)=x^3+kx^2=12x-4
2007-04-15 11:50:58 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
(x-2)( x^2 +2) = x^3+kx^2+12x-4
we know coeff of x^2 is same as that of x^3
we know const must be 2 to get the -4
(x-2)( x^2 -5x +2) = x^3+kx^2+12x-4
it must be -5 to get the 12x
so k = -5
2007-04-15 11:57:33 · answer #1 · answered by hustolemyname 6 · 0⤊ 1⤋
f(x)=x^3+kx^2-12x+4
Divide 1, k, -12, 4 by 2 and you get
1, k+2, 2k-8, 4k-12
Since x-2 is a factor the remainder for the division is 0.
4k-12=0
k=3
2007-04-15 11:59:05 · answer #2 · answered by dcl 3 · 0⤊ 1⤋
2|1_-12__k___4
. |2__6__12__-4
. 3___6__-2__0
f(x)=x^3+kx^2-12x+4
The result has to be 0, so k has to be -14.
2007-04-15 12:12:26 · answer #3 · answered by SG 2 · 0⤊ 0⤋