Advertisements
Advertisements
Question
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 |
Advertisements
Solution
Quotient = 3y2 + 2y + 2
Remainder = 4y2 + 25y + 4
Divisor = 2y3 + 1
Divisor x Quotient + Remainder = (2y3 + 1) (3y2 + 2y + 2) + 4y2 + 25y + 4
= 6y5 + 4y4 + 4y3 + 3y2 + 2y + 2 + 4y2 + 25y + 4
= 6y5 + 4y4 + 4y3 + 7y2 + 27y + 6
= Dividend
Thus,
Divisor x Quotient + Remainder = Dividend
Hence verified.
APPEARS IN
RELATED QUESTIONS
Write the degree of each of the following polynomials.
5x2 − 3x + 2
Write the degree of each of the following polynomials.
Write each of the following polynomials in the standard form. Also, write their degree.
Divide 15m2n3 by 5m2n2.
Divide\[- x^6 + 2 x^4 + 4 x^3 + 2 x^2\ \text{by} \sqrt{2} x^2\]
Divide 4z3 + 6z2 − z by −\[\frac{1}{2}\]
Using division of polynomials, state whether
4x − 1 is a factor of 4x2 − 13x − 12
Divide: 8x − 10y + 6c by 2
Divide: −14x6y3 − 21x4y5 + 7x5y4 by 7x2y2
Divide: (32y2 – 8yz) by 2y
