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प्रश्न
Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:
3x2 + 4x + 5, x − 2
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उत्तर
\[\frac{3 x^2 + 4x + 5}{x - 2}\]
\[ = \frac{3x(x - 2) + 10(x - 2) + 25}{(x - 2)}\]
\[ = \frac{(x - 2)(3x + 10) + 25}{(x - 2)}\]
\[ = (3x + 10) + \frac{25}{(x - 2)}\]
\[\text{Therefore,} \]
\[\text{quotient = 3x + 10 and remainder = 25 .} \]
संबंधित प्रश्न
Write the degree of each of the following polynomials.
5x2 − 3x + 2
Which of the following expressions are not polynomials?
x2 + 2x−2
Write each of the following polynomials in the standard form. Also, write their degree.
(y3 − 2)(y3 + 11)
Divide \[y^4 - 3 y^3 + \frac{1}{2} y^2 by 3y\]
Divide m3 − 14m2 + 37m − 26 by m2 − 12m +13.
Divide 9x4 − 4x2 + 4 by 3x2 − 4x + 2 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 |
| 6y5 + 4y4 + 4y3 + 7y2 + 27y + 6 | 2y3 + 1 |
Using division of polynomials, state whether
2y − 5 is a factor of 4y4 − 10y3 − 10y2 + 30y − 15
Using division of polynomials, state whether
3y2 + 5 is a factor of 6y5 + 15y4 + 16y3 + 4y2 + 10y − 35
Statement A: If 24p2q is divided by 3pq, then the quotient is 8p.
Statement B: Simplification of `((5x + 5))/5` is 5x
