Use synthetic substitution to find the value of f(-2) for f(x)=x^3-3x^2-x-9.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The value of f(x) = x^3 - 3x^2 - x - 9 for x = -2 can be determined in the following way:

Write the value of x and the coefficients of the polynomial in the following manner.

-2 | 1___-3___-1___-9

Leave a space below this and draw a line

-2 | 1___-3___-1___-9

 

---------------------------------

Take the first coefficient as it is.

-2 | 1___-3___-1___-9

 

--------------------------------

____1

Multiply the number -2 with the first value and write the result below the second coefficient.

-2 | 1___-3___-1___-9

 ___1___-2

--------------------------------

___1

Write the sum of the two below the line

-2 | 1___-3___-1___-9

 ___1___-2

------------------------------

_______-5

Multiply the number with the sum and write the value obtained below the next coefficient; determine the sum and continue with the process.

-2 | 1___-3___-1___-9

 _______-2___10__ -18

---------------------------------

____1__-5____9____-27

The final number below the line is the required value of f(-2).

For f(x) = x^3 - 3x^2 - x - 9, f(-2) = -27

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