Question

Find the value of k,if (x-2) is a factor of4x^3+3x^2-4x+ k

Answer 1

(x-2) is factor of the the polynomial
x-2=0
x=2
on putting x=2
p(x() should be zero
so
$4 { {x}^{3} } + 3 {x}^{2} - 4x + k$
$4 \times {2}^{3} + 3 \times {2}^{2} - 4 \times 2 + k = 0$
4×8+3×4-8+k=0
32+12-8+k=0
36+k=0
k=-36