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 each of the following polynomials in the standard form. Also, write their degree.
x2 + 3 + 6x + 5x4
Write each of the following polynomials in the standard form. Also, write their degree.
Divide 4y2 + 3y +\[\frac{1}{2}\] by 2y + 1.
Divide 14x3 − 5x2 + 9x − 1 by 2x − 1 and find the quotient and remainder
Divide 30x4 + 11x3 − 82x2 − 12x + 48 by 3x2 + 2x − 4 and find the quotient and remainder.
Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.
| Dividend | Divisor |
| 34x − 22x3 − 12x4 − 10x2 − 75 | 3x + 7 |
Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.
| Dividend | Divisor |
| 15y4 − 16y3 + 9y2 −\[\frac{10}{3}\] y+6 | 3y − 2 |
Using division of polynomials, state whether
x + 6 is a factor of x2 − x − 42
Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:
3x2 + 4x + 5, x − 2
Find whether the first polynomial is a factor of the second.
x + 1, 2x2 + 5x + 4
