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Divide the polyinomals U(x)=9x^4-4x^2+4 by the …

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Divide the polyinomals U(x)=9x^4-4x^2+4 by the polynomialsV(x) =3x^2 +x-1, Also find quotient and remainder

Posted by Tonika Bhalai 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Divide the polynomial u(x) = 9x⁴ - 4x² + 4 by the polynomial v(x) = 3x² + x - 1 by using long division method, we get

Clearly, quotient q(x) = 3x² - x and remainder r(x) = -x + 4.
Also, v(x) q(x) + r(x) = (3x² + x - 1) (3x² - x) + (-x + 4)
= 9x⁴ + 3x³ - 3x² - 3x³ - x² + x - x + 4
= 9x⁴ + 0x³ - 4x² + 0x + 4
= 9x⁴ - 4x² + 4
i.e. u(x) = v(x) q(x) + r(x) = 9x⁴ - 4x² + 4 = u(x)
or, Dividend = Quotient {tex}\times{/tex} Divisor + Remainder

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CBSE > Class 10 > Mathematics