CLASS-10
REMINDER 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

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