Question

Find the value of a when x^3-ax^2+6x-a is exactly divisibal by x+2

Answer 1

$x + 2 = 0 \\ x = - 2\\ let .\: p(x) \: = {x}^{3} - a {x}^{2} + 6x - a = 0 \\ p( - 2) = ({ - 2})^{3} - a( { - 2})^{2} + 6( - 2) - a = 0 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = > - 8 - 4a - 12 - a = 0\\ \: \: \: \: \: \: \: \: \: \: \: \: \: = > - 20 - 3a = 0 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = > - 20 = 3a \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = > 3a = - 20 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = > a = - 20 \div 3$