using reminder theorem find the remainder when 2x^3-4x^2+x-5 is divided by x-3 and verify by actual division
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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+4The coefficients in descending order from the variable with the highestexponent 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)
-------------- 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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