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 |
| 15z3 − 20z2 + 13z − 12 | 3z − 6 |
Advertisements
उत्तर
\[\text{Quotient} = 5 z^2 + \frac{10}{3}z + 11\]
\[\text{Remainder} = 54\]
\[\text{Divisor} = 3z - 6\]
\[\text{Divisor} \times \text{Quotient} + \text{Remainder} = (3z - 6)\left( 5 z^2 + \frac{10}{3}z + 11 \right) + 54\]
\[ = 15 z^3 + 10 z^2 + 33z - 30 z^2 - 20z - 66 + 54\]
\[ = 15 z^3 - 20 z^2 + 13z - 12\]
\[ = \text{Dividend}\]
\[Thus, \]
\[\text{Divisor} \times \text{Quotient} + \text{Remainder} = \text{Dividend}\]
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
Which of the following expressions are not polynomials?
Write each of the following polynomials in the standard form. Also, write their degree.
Divide x + 2x2 + 3x4 − x5 by 2x.
Divide 3y4 − 3y3 − 4y2 − 4y by y2 − 2y.
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
z2 + 3 is a factor of z5 − 9z
Using division of polynomials, state whether
2x2 − x + 3 is a factor of 6x5 − x4 + 4x3 − 5x2 − x − 15
Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:
x4 − x3 + 5x, x − 1
