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What GOAL 1 - ClassZone
Page 1 of 2 The remainder and FactorTheoremsDIVIDINGPOLYNOMIALSWhen you divide a polynomial (x) by a divisor d(x), you get a quotient polynomialq(x) and a remainder polynomial r(x). We write this as d((xx)) =q(x)+ dr((xx)) . Thedegree of the remainder must be less than the degree of the divisor. Example 1 shows how to divide polynomials using a method called Using Polynomial Long DivisionDivide 2x4+ 3x3+ 5x 1 by x2 2x+ division in the same format you would use when dividing numbers. Include a 0 as the coefficient of x2. 2xx24 7xx23 1x02x2 2x2+ 17x+10x2 2x+2 2 x4 + 3 x3 + 1 0 x2 + 1 5 x 1 1 2x4 4x3+ 14x2 Subtract2x2(x2 2x+2).7x3 14x2+ 15x7x3 14x2+ 14xSubtract7x(x2 2x+2).10x2 19x 1110x2 20x+ 20 Subtract10(x2 2x+2).11x 21remainderWrite the result as follows. = 2x2+ 7x+ 10+ CHECK You can check the result of a division problem by multiplying the divisorby the quotient and adding the remainder .
Page 1 of 2 6.5 The Remainder and Factor Theorems 353 In the activity you may have discovered that ƒ(2) gives you the remainder when ƒ(x)is divided by x º 2. This result is generalized in the remainder theorem. You may also have discovered in the activity that synthetic substitution gives the
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