# CLASS-10REMINDER THEOREM & FACTOR THEOREM - VALUE OF A POLYNOMIAL

Value of a Polynomial f(x) at x = α

The value of a polynomial f(x) at x = α is obtained by substituting x = α in the given polynomial and it is denoted by f(α).

Example.1) If f(x) = 3x³ + 2x² - 6x – 11, find f(3)

Ans.) We have f(x) = 3x³+ 2x²- 6x – 11

As per given condition, f(3) = {(3 X 3³) + (2 X 3²) – (6 X 3) – 11}

= {(3 X 27) + (2 X 9) – 18 – 11}

= {(81 + 18) – (18 + 11)}

= (99 – 29)

= 70        (Ans.)

Example.2) If f(x) = 5x³- 2x²+ 8x – 15, find f(- 2)

Ans.) We have f(x) = 5x³- 2x²+ 8x – 15

As per the given condition,

f(-2) = [{5 X (-2)³} – {2 X (-2)²} + {8 X (-2)} – 15]

= [{5 X (-8)} – (2 X 4) + (-16) – 15]

= (- 40 – 8 – 16 – 15)

= -79                  (Ans.)

Example.3) If f(x) = 7x²- 3x + 8, find f(-1/2)

Ans.) We have f(x) = 7x²- 3x + 8

As per the given condition,

1                   1                     1

f(- -----) = [{7 X (- -----)²} – {3 X ( - -----)} + 8]

2                   2                     2

7           3

= ------- + ------- + 8

4           2

14 + 3

= ---------- + 8

4

17 + 32

= ----------

4

49

= -------      (Ans.)

4