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โœ”๏ธ Class: 10th
โœ”๏ธ Subject: Maths
โœ”๏ธ Chapter: Polynomials Chapter 2
โœ”๏ธ Topic Name: Division Algorithm for Polynomials
โœ”๏ธ Topics to be Covered: Class 10 Maths Chapter 2 - Division Algorithm for Polynomials - Polynomials

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Type - 4
If the zeros of the polynomial f(x) = x3 - 3x2 + x + 1 are a - b, a, a + b. Find a and b. (a and b are real numbers)
From Euclidโ€™s division lemma, we know that
Dividend = (Divisor x Quotient) + Remainder

Applying the same to polynomials,
If f(x) and g(x) are any two polynomials with g(x) โ‰  0, then we can find polynomials q(x) and r(x) such that
f(x) = q(x) x g(x) + r(x),
Degree of r(x) less than Degree of g(x)

If r(x) = 0, then polynomial g(x) is a factor of polynomial f(x).