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 |
| 4y3 + 8y + 8y2 + 7 | 2y2 − y + 1 |
Advertisements
Solution
Quotient = 2y + 5
Remainder = 11y + 2
Divisor = 2y2 - y + 1
Divisor x Quotient + Remainder = (2y2 - y + 1) (2y + 5) + 11y + 2
= 4y3 +10y2 - 2y2 - 5y + 2y + 5 + 11y + 2
= 4y3 + 8y2 + 8y + 7
= Dividend
Thus,
Divisor x Quotient + Remainder = Dividend
Hence verified.
RELATED QUESTIONS
Write the degree of each of the following polynomials.
Which of the following expressions are not polynomials?
Which of the following expressions are not polynomials?
Write each of the following polynomials in the standard form. Also, write their degree.
Divide\[\sqrt{3} a^4 + 2\sqrt{3} a^3 + 3 a^2 - 6a\ \text{by}\ 3a\]
Divide 2y5 + 10y4 + 6y3 + y2 + 5y + 3 by 2y3 + 1.
Divide 6x3 + 11x2 − 39x − 65 by 3x2 + 13x + 13 and find the quotient and remainder.
Using division of polynomials, state whether
x + 6 is a factor of x2 − x − 42
Divide:
(a2 + 2ab + b2) − (a2 + 2ac + c2) by 2a + b + c
The denominator of a fraction exceeds Its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, we get `3/2`. Find the original fraction.
