Question

What number must be subtracted from the polynomial x³ − 6x² + 2x so that (x – 1) is a factor of resulting polynomial?

Answer 1

Let the number subtracted be k

f(x) = x³ − 6x² + 2x − k

Let x – 1 = 0

x = 1

f(1) = 1³ − 6(1)² + 2(1) − k

= 1 − 6 + 2 − k

= −3 − k

Set the remainder f(1) equal to zero to find the value of k

f(1) = 0

−3 − k = 0

k = −3

∴ The number that must be subtracted is −3.