Question

if p(x)=2x^3+5x^2-3x-2 is divided by (x-1) then reminder is​

Answer 1

For the remainder theorem we generally use synthetic division.

If (x+2) is a factor of P(x) then x=-2 will be a zero of P(x)

we have P(x) = 2x2-3x+4

The coefficients in descending order from the variable with the highest

exponent to the constant are 2, -3, 4

Write the -2 on the left with a diagonal separating it from the coefficients:

-2 / 2 -3 4 1)bring down the first coefficient (2)

-4 14 2)multiply that by the -2 giving -4

-------------- 3)bring that product up under the next coefficient

2 -7 18 add down.

4 Repeat to the end. Last number is the remainder

The remainder is 18. The remainder theorem says that f(-2) = 18

The polynomial we get when we divide is

(2x2 -3x+4)/(x+2)= 2x-7+ 18/(x+2)

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