Advertisements
Advertisements
प्रश्न
Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:
10x2 − 7x + 8, 5x − 3
Advertisements
उत्तर
\[ \frac{10 x^2 - 7x + 8}{5x - 3}\]
\[ = \frac{2x(5x - 3) - \frac{1}{5}(5x - 3) + \frac{47}{5}}{(5x - 3)}\]
\[ = \frac{(5x - 3)(2x - \frac{1}{5}) + \frac{47}{5}}{(5x - 3)}\]
\[ = (2x - \frac{1}{5}) + \frac{\frac{47}{5}}{5x - 3}\]
\[\text{Therefore,} \]
\[\text{quotient }= 2x - \frac{1}{5} \text{and remainder} = \frac{47}{5} . \]
APPEARS IN
संबंधित प्रश्न
Write the degree of each of the following polynomials.
2x2 + 5x2 − 7
Divide −72a4b5c8 by −9a2b2c3.
Divide\[- x^6 + 2 x^4 + 4 x^3 + 2 x^2\ \text{by} \sqrt{2} x^2\]
Divide 9x2y − 6xy + 12xy2 by −\[\frac{3}{2}\]
Divide m3 − 14m2 + 37m − 26 by m2 − 12m +13.
Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.
| Dividend | Divisor |
| 15z3 − 20z2 + 13z − 12 | 3z − 6 |
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 |
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.
What must be added to x4 + 2x3 − 2x2 + x − 1 , so that the resulting polynomial is exactly divisible by x2 + 2x − 3?
Divide:
x4 − y4 by x2 − y2
