Question

Show that x⁵²-21x+20 is divisible by x− 1.

Answer 1

given equation,

x⁵²-21 x+20

A number to be divisible by the another number means that on dividing the remainder should be zero.

if x⁵²-21 x+20 is divisible by x− 1 means that x-1 should completely divide the equation.

so,

x -1 = 0

x = 1

x⁵²-21 x+20 to be divisible it should be equal to zero when x = 1

putting x = 1

= (1)⁵²-21 (1)+20

= 1 - 21 + 20

= 21 -21

= 0

hence x = 1 is the root of the equation

so, x⁵²-21 x+20 is divisible by x− 1.