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प्रश्न
State Division Algorithm for Polynomials.
उत्तर
“If f(x) and g(x) are two polynomials such that degree of f(x) is greater than degree of g(x) where g(x) ≠ 0, there exists unique polynomials q(x) and r(x) such that
f(x) = g(x) × q(x) + r(x),
where r(x) = 0 or degree of r(x) ˂ degree of g(x).
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संबंधित प्रश्न
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following
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Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following
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On dividing x3 – 3x2 + x + 2 by a polynomial g(x), the quotient and remainder were x – 2 and –2x + 4, respectively. Find g(x)
Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm
deg p(x) = deg q(x)
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If (x + a) is a factor of `(2x^2 + 2ax + 5x + 10)`, then find the value of a.
Find all zeros of the polynomial 3x3 + 10x2 − 9x − 4 if one of its zero is 1.
Find the quotient and remainder of the following.
(4x3 + 6x2 – 23x + 18) ÷ (x + 3)
For which values of a and b, are the zeroes of q(x) = x3 + 2x2 + a also the zeroes of the polynomial p(x) = x5 – x4 – 4x3 + 3x2 + 3x + b? Which zeroes of p(x) are not the zeroes of q(x)?
