Question

find the value of a if 2x²-3x is a factor of x³+2x²+ax- 3a

Answer 1

Step-by-step explanation:

$2 {x}^{2} - 3x \: is \: a \: factor \\ that \: is \: \\ x(2x - 3) = 0 \\x = 0 \: or \: \frac{3}{2}$

${x}^{3} + 2 {x}^{2} + ax - 3a = 0 \: at \: x = 0 \\ 0 + 0 + 0 - 3a = 0 \\ a = 0$

now, if it is a factor of polynomial ,then it will satisfy the eqn

put zero in eqn.