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प्रश्न
Divide \[y^4 - 3 y^3 + \frac{1}{2} y^2 by 3y\]
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उत्तर
\[\frac{y^4 - 3 y^3 + \frac{1}{2} y^2}{3y}\]
\[ = \frac{y^4}{3y} - \frac{3 y^3}{3y} + \frac{\frac{1}{2} y^2}{3y}\]
\[ = \frac{1}{3} y^{(4 - 1)} - y^{(3 - 1)} + \frac{1}{6} y^{(2 - 1)} \]
\[ = \frac{1}{3} y^3 - y^2 + \frac{1}{6}y\]
संबंधित प्रश्न
Write each of the following polynomials in the standard form. Also, write their degree.
(y3 − 2)(y3 + 11)
Divide 4y2 + 3y +\[\frac{1}{2}\] by 2y + 1.
Divide 3y4 − 3y3 − 4y2 − 4y by y2 − 2y.
Divide 2y5 + 10y4 + 6y3 + y2 + 5y + 3 by 2y3 + 1.
Divide 14x3 − 5x2 + 9x − 1 by 2x − 1 and find the quotient and remainder
Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.
| Dividend | Divisor |
| 14x2 + 13x − 15 | 7x − 4 |
Using division of polynomials, state whether
3y2 + 5 is a factor of 6y5 + 15y4 + 16y3 + 4y2 + 10y − 35
Find whether the first polynomial is a factor of the second.
4x2 − 5, 4x4 + 7x2 + 15
Divide:
x4 − y4 by x2 − y2
The denominator of a fraction exceeds Its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, we get `3/2`. Find the original fraction.
