Advertisements
Advertisements
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 |
Advertisements
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.
APPEARS IN
संबंधित प्रश्न
Which of the following expressions are not polynomials?
x2 + 2x−2
Divide 6x3y2z2 by 3x2yz.
Divide x + 2x2 + 3x4 − x5 by 2x.
Divide −21 + 71x − 31x2 − 24x3 by 3 − 8x.
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
x + 6 is a factor of x2 − x − 42
Using division of polynomials, state whether
4x − 1 is a factor of 4x2 − 13x − 12
What must be added to x4 + 2x3 − 2x2 + x − 1 , so that the resulting polynomial is exactly divisible by x2 + 2x − 3?
7ab3 ÷ 14ab = 2b2
Divide: 81(p4q2r3 + 2p3q3r2 – 5p2q2r2) by (3pqr)2
