For the polynomial  f (x) = x5+ 2x3+9x2-12x-30, use synthetic division to find  f (-2).

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justaguide | College Teacher | (Level 2) Distinguished Educator

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Using synthetic division to find f(-2) is done in this way:

First write the coefficients of all the values of x in the expression that you are dividing starting from the largest power at the left and moving to the lower power as you move to the right. The -2 is written outside.

Now take down the 1. Multiply it by -2, and write it below the next coefficient. Add the two numbers. Again multiply the sum by -2 and move towards the right.

The steps explained above have been implemented below.

 

-2 | 1   0   2     9     -12   -30

|     -2   4   -12     6      12

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

=>  1  -2   6   -3      -6     -18

 

Once we are done, we get the coefficient of the terms that make up the quotient and the remainder.

The required quotient is x^4 - 2x^3 + 6x^2 - 3x - 6.

And the remainder is -18.

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