Question

fins the value of a if (x-a) is a factor of x³ -a²x+x+2

Answer 1

x-a=0
=>x=a
put x=a in the equation x³-a²x+x+2
=>a³-a²(a)+a+2=0
=>a³-a³+a+2=0
=>a+2=0
=>a=-2

Answer 2

$x - a = 0 \\ x = a$
Putting this value in the given equation,
${x}^{3} - {a}^{2} x + x + 2 = 0 \\ {a}^{3} - {a}^{2} \times a + a + 2 = 0 \\ {a}^{3} - {a}^{3} + a + 2 = 0 \\ a + 2 = 0 \\ a = - 2$