Created on 2024-06-20Asked by Olivia Ramirez (Solvelet student)
Perform polynomial long division to divide f(x)=x3+2x2−x−2 by g(x)=x−1.
Solution
To perform polynomial long division to divide f(x)=x3+2x2−x−2 by g(x)=x−1: 1. Write the dividend f(x) and divisor g(x): x−1x3+2x2−x−2 2. Divide the leading term of the dividend by the leading term of the divisor: \begin{array}{r|l} x - 1 & x^3 + 2x^2 - x - 2 \\ \cline{2-2} & x^3 - x^2 \\ \end{array} 3. Multiply the divisor by the result of step 2 and subtract from the dividend: \begin{array}{r|l} x - 1 & x^3 + 2x^2 - x - 2 \\ \cline{2-2} & x^3 - x^2 \\ \cline{2-2} & 3x^2 - x - 2 \\ \end{array} 4. Repeat steps 2 and 3 until the degree of the remainder is less than the degree of the divisor. 5. The result is the quotient q(x) and the remainder r(x). Therefore, the quotient is x2+x+1 and the remainder is −1. Solved on Solvelet with Basic AI Model
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DefinitionPolynomial long division is a method for dividing a polynomial by another polynomial of lesser degree. It extends the long division algorithm for numbers to polynomials. It is a process where there is the division and division and division... (Multiplications and subtractions) until we have a remainder. Eg:- x3+2x2+4x+4 divided by x+1 gives quotient x2+x+3 and remainder 1
