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Polynomial Division easy solution CBSEICSE Class 9th amp 10th Algebra Mathematics
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What is Polynomial Division? • Polynomial division is a method for dividing one polynomial (the dividend) by another polynomial (the divisor) of the same or lower degree. It's a generalization of the long division method you might be familiar with from arithmetic. • The Division Algorithm • When you divide a polynomial p(x) by another polynomial g(x) (where g(x) ≠ 0), you get a quotient q(x) and a remainder r(x). This can be expressed as: • p(x) = q(x) * g(x) + r(x) • where: • p(x) is the dividend • g(x) is the divisor • q(x) is the quotient • r(x) is the remainder (which is either 0 or has a degree less than g(x)) • Long Division Method • Here's how to perform polynomial long division: • Arrange: Write the dividend and divisor in descending order of their exponents. • Divide: Divide the first term of the dividend by the first term of the divisor. Write the result above the dividend. • Multiply: Multiply the divisor by the term you just wrote in the quotient. Write the result below the dividend. • Subtract: Subtract the result from the dividend. • Bring Down: Bring down the next term from the dividend. • Repeat: Repeat steps 2-5 until there are no more terms to bring down. • The final result will be the quotient and the remainder. • Important Points • If the remainder is 0, the divisor is a factor of the dividend. • If the degree of the remainder is less than the degree of the divisor, the division is complete. • If the degree of the remainder is equal to or greater than the degree of the divisor, you can continue the division process. • Additional Notes • There's a shorthand method called synthetic division that can be used for dividing by linear binomials (of the form x - a). • Polynomial division is a fundamental tool in algebra and has applications in various areas of mathematics and science. • #polynomials #division #polynomialdivision #polynomialsclass10 #polynomialsexercise2 #polynomialclass9 #polynomialsclass9th #polynomialsclass9 #polynomial #mathematics #mathematician #mathematical #mathe #solutionacademyindia #mathtricks #maths #mathstricks #mathematicsclasses #cbsemaths #icsemaths #iit #ssc #ssc #nda #basicmaths #basicmathtrick
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