Advertisements
Advertisements
Question
Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:
3x2 + 4x + 5, x − 2
Solution
\[\frac{3 x^2 + 4x + 5}{x - 2}\]
\[ = \frac{3x(x - 2) + 10(x - 2) + 25}{(x - 2)}\]
\[ = \frac{(x - 2)(3x + 10) + 25}{(x - 2)}\]
\[ = (3x + 10) + \frac{25}{(x - 2)}\]
\[\text{Therefore,} \]
\[\text{quotient = 3x + 10 and remainder = 25 .} \]
APPEARS IN
RELATED QUESTIONS
Divide the given polynomial by the given monomial.
8(x3y2z2 + x2y3z2 + x2y2z3) ÷ 4x2y2z2
Divide\[\sqrt{3} a^4 + 2\sqrt{3} a^3 + 3 a^2 - 6a\ \text{by}\ 3a\]
Divide x2 + 7x + 12 by x + 4.
Divide 4y2 + 3y +\[\frac{1}{2}\] by 2y + 1.
Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.
| Dividend | Divisor |
| 6y5 − 28y3 + 3y2 + 30y − 9 | 2y2 − 6 |
Using division of polynomials, state whether
2x2 − x + 3 is a factor of 6x5 − x4 + 4x3 − 5x2 − x − 15
Find the value of a, if x + 2 is a factor of 4x4 + 2x3 − 3x2 + 8x + 5a.
Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:
10x2 − 7x + 8, 5x − 3
Find whether the first polynomial is a factor of the second.
y − 2, 3y3 + 5y2 + 5y + 2
Divide: 15a3b4 − 10a4b3 − 25a3b6 by −5a3b2
