Question

$the \: value \: of \: k \: if \: x - 1 \: is \: a \:factor \: of \: 4 {x}^{3} + 3 {x}^{2} - 4x + k$

Answer 1

Zero of ( x - 1 ) = 1.

P( x ) =  4 x ^ 3 + 3 x ^ 2 - 4 x + k

P ( 1 ) = 4 * 1 ^ 3 + 3 * 1 ^ 2 - 4 * 1 + k = 0

              4 * 1 + 3 * 1 - 4 + k = 0

              4 + 3 - 4 + k = 0

              3 + k = 0

              k = - 3

Answer 2

If x-1 is a factor of
4x³+3x²-4x+k=0
4x³+3x²-4x=-k

x-1=0
x=1,

Putting 1 in the equation we get,
4*1³+3*1²-4*1+k=0
4+3-4+k=0
7-4+k=0
3+k=0
k=-3.

Hope it helps.
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