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प्रश्न
Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:
y4 + y2, y2 − 2
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उत्तर
\[\frac{y^4 + y^2}{y^2 - 2}\]
\[ = \frac{y^2 ( y^2 - 2) + 3( y^2 - 2) + 6}{y^2 - 2}\]
\[ = \frac{( y^2 - 2)( y^2 + 3) + 6}{y^2 - 2}\]
\[ = ( y^2 + 3) + \frac{6}{y^2 - 2}\]
\[\text{Therefore, quotient} = y^2 + 3 \text{and remainder} = 6 .\]
संबंधित प्रश्न
Write the degree of each of the following polynomials.
2x2 + 5x2 − 7
Which of the following expressions are not polynomials?
x2 + 2x−2
Which of the following expressions are not polynomials?
Divide 24a3b3 by −8ab.
Divide −21abc2 by 7abc.
Divide x2 + 7x + 12 by x + 4.
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 |
Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.
| Dividend | Divisor |
| 34x − 22x3 − 12x4 − 10x2 − 75 | 3x + 7 |
Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:
x4 − x3 + 5x, x − 1
Find whether the first polynomial is a factor of the second.
x + 1, 2x2 + 5x + 4
