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प्रश्न
Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.
| Dividend | Divisor |
| 15y4 − 16y3 + 9y2 −\[\frac{10}{3}\] y+6 | 3y − 2 |
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उत्तर
Quotient = \[5 y^3 - 2 y^2 + \frac{5}{3}y\]
Remainder = 6
Divisor = 3y - 2
Divisor x Quotient + Remainder = (3y - 2) (5y3 - 2y2 +
Divisor x Quotient + Remainder = Dividend
Hence verified.
संबंधित प्रश्न
Write the degree of each of the following polynomials.
2x + x2 − 8
Write the degree of each of the following polynomials.
Which of the following expressions are not polynomials?
Divide 4y2 + 3y +\[\frac{1}{2}\] by 2y + 1.
Divide x4 + x2 + 1 by x2 + x + 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 |
Divide `15 y^4 + 16 y^3 + 10-3 y - 9y^2 - 6` by 3y − 2. Write down the coefficients of the terms in the quotient.
Find whether the first polynomial is a factor of the second.
x + 1, 2x2 + 5x + 4
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.
