# EVALUATE POLYNOMIALS USING SYNTHETIC DIVISION

## About "Evaluate polynomials using synthetic division"

Evaluate polynomials using synthetic division :

Here we are going to see how to evaluate polynomials using synthetic division.

Let us see some example problems to understand this concept.

Step 1:  Arrange the dividend in the descending powers of x and then write the coefficients of dividend in the first zero. Insert 0 for missing terms.

Step 2:  Write the number in which we have to divide in the left side.

Step 3:  Put 0 for the first entry in the second row.

Step 4:  Write down the quotient and remainder accordingly.

Example 1 :

If g(u) = 20u²– 31u – 32, use synthetic division to find g(2).

Solution : Hence the value of g(2) is -14.

Example 2 :

If f(x) =  x³ - 2 x² - 5 x + 6 use synthetic division to find f(-1).

Solution : Hence the value of f(-1) is 8.

Example 3 :

If f(t) = 4 t³ - 5 t² + 7 t - 6 use synthetic division to find f(2).

Solution : Hence the value of f(2) is 20.

Example 4 :

If g(u) = u³ - 7 u + 6 use synthetic division to find f(-3).

Solution :

Since u² term is missing, we have to put zero for the missing term. Hence the value of g(-3) is 0.

Example 5 :

If f(t) = t³  + 13 t² + 32 t + 20  use synthetic division to find f(-1).

Solution : Hence the value of f(-1) is 0.

Example 6 :

If f(x) = x³ - 10 x² - x + 10  use synthetic division to find f(7).

Solution : Hence the value of f(7) is -144.

Example 7 :

If f(x) = 2 x³ + 11 x² - 7 x - 6  use synthetic division to find f(-5).

Solution : Hence the value of f(7) is 54.

Example 8 :

If f(x) =  x³ - 23 x² + 142 x - 120  use synthetic division to find f(-1).

Solution : Hence the value of f(-1) is -286.

Example 9 :

If f(x) = 2 x³ + 11 x² - 7 x - 6  use synthetic division to find f(3).

Solution : Hence the value of f(3) is 126.

Example 10 :

If f(x) = 2 x³ + 11 x² + 5 x - 2  use synthetic division to find f(1).

Solution : Hence the value of f(1) is 16.

After having gone through the stuff given above, we hope that the students would have understood "Evaluate polynomials by using synthetic division".

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