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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 |
| 6y5 − 28y3 + 3y2 + 30y − 9 | 2y2 − 6 |
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उत्तर
Quotient = \[3 y^3 - 5y + \frac{3}{2}\]
Remainder = 0
Divisor = 2y2 - 6
Divisor x Quotient + Remainder =
\[(2 y^2 - 6) \left( 3 y^3 - 5y + \frac{3}{2} \right) + 0\]
\[ = 6 y^5 - 10 y^3 + 3 y^2 - 18 y^3 + 30y - 9\]
\[ = 6 y^5 - 28 y^3 + 3 y^2 + 30y - 9\]
= Dividend
Thus, Divisor x Quotient + Remainder = Dividend
Hence verified.
संबंधित प्रश्न
Write the degree of each of the following polynomials.
Which of the following expressions are not polynomials?
Write each of the following polynomials in the standard form. Also, write their degree.
x2 + 3 + 6x + 5x4
Write each of the following polynomials in the standard form. Also, write their degree.
Divide 5z3 − 6z2 + 7z by 2z.
Divide x4 − 2x3 + 2x2 + x + 4 by x2 + x + 1.
Using division of polynomials, state whether
x + 6 is a factor of x2 − x − 42
Using division of polynomials, state whether
2y − 5 is a factor of 4y4 − 10y3 − 10y2 + 30y − 15
Find whether the first polynomial is a factor of the second.
4y + 1, 8y2 − 2y + 1
Statement A: If 24p2q is divided by 3pq, then the quotient is 8p.
Statement B: Simplification of `((5x + 5))/5` is 5x
