Use synthetic division to find p (-3) for p (x)=x^4-2x^3-4x+4

The value of p(-3) is 151.

Explanation:

According to the remainder theorem of the polynomial if the polynomial is divide by (x-c), then the remainder is equal to f(c).

The given function is,

If can be written as,

The coefficients of the polynomial are 1,-2,0,-4 and 4.

We have to divide the polynomial by (x+3), Write the coefficients in top row and write -3 on left side.

Write fist coefficient as it is, in bottom row.

Multiply -3 by 1 and write the result (i.e., -3) in middle row below the coefficient of second element. Now add -2 and -3 and write the result (i.e.,-5 ) in bottom row.

Apply to process again and again until the coefficients remains as shown in the below figure.

The elements of bottom line show the coefficients of quotient polynomial and remainder after dividing the polynomial by (x+3).

Only the last element represents the remainder.

Since remainder is 151, so by remainder theorem we get f(-3)=151.

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