Find the remainder when f(x) = x³ - 14x² + 51x - 22 is divided by x - 7.
36, 8, - 8, - 36

Solution:

The Remainder theorem states:

Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number.

If p(x) is divided by the linear polynomial x - a then the remainder is p(a).

As per the remainder theorem the zero of the polynomial x - 7 is 7.

Therefore if we substitute the value of x =7 in the polynomial f(x) we will get the remainder.

f(7) = (7)³ - 14(7)² + 51(7) - 22

= 343 - 14 × 49 + 357 - 22

= 700 - 686 -22

= -8

Hence on dividing f(x) = x³ - 14x² + 51x - 22 by x - 7 the remainder is -8.

Find the remainder when f(x) = x³ - 14x² + 51x - 22 is divided by x - 7.
36, 8, - 8, - 36

Summary:

The remainder on dividing polynomial f(x) = x³ - 14x² + 51x - 22 by x - 7 is -8.