Advertisements
Advertisements
Question
Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:
10x2 − 7x + 8, 5x − 3
Advertisements
Solution
\[ \frac{10 x^2 - 7x + 8}{5x - 3}\]
\[ = \frac{2x(5x - 3) - \frac{1}{5}(5x - 3) + \frac{47}{5}}{(5x - 3)}\]
\[ = \frac{(5x - 3)(2x - \frac{1}{5}) + \frac{47}{5}}{(5x - 3)}\]
\[ = (2x - \frac{1}{5}) + \frac{\frac{47}{5}}{5x - 3}\]
\[\text{Therefore,} \]
\[\text{quotient }= 2x - \frac{1}{5} \text{and remainder} = \frac{47}{5} . \]
RELATED QUESTIONS
Divide the given polynomial by the given monomial.
(5x2 − 6x) ÷ 3x
Divide the given polynomial by the given monomial.
(3y8 − 4y6 + 5y4) ÷ y4
Write the degree of each of the following polynomials.
Divide 6x3y2z2 by 3x2yz.
Divide 4z3 + 6z2 − z by −\[\frac{1}{2}\]
Divide 3x3y2 + 2x2y + 15xy by 3xy.
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 |
| 4y3 + 8y + 8y2 + 7 | 2y2 − y + 1 |
Using division of polynomials, state whether
4x − 1 is a factor of 4x2 − 13x − 12
Find whether the first polynomial is a factor of the second.
4x2 − 5, 4x4 + 7x2 + 15
