Advertisements
Advertisements
Question
Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:
x4 − x3 + 5x, x − 1
Advertisements
Solution
\[\frac{x^4 {-x}^3 +5x}{x-1}\]
\[ = \frac{x^3 (x-1)+5(x-1)+5}{x-1}\]
\[ = \frac{{(x-1)(x}^3 +5)+5}{x-1}\]
\[ {=(x}^3 +5)+ \frac{5}{x - 1}\]
\[\text{Therefore, quotient} = x^3 +5\ \text{and remainder = 5 .}\]
APPEARS IN
RELATED QUESTIONS
Which of the following expressions are not polynomials?
Divide 6x3y2z2 by 3x2yz.
Simplify:\[\frac{32 m^2 n^3 p^2}{4mnp}\]
Divide\[- x^6 + 2 x^4 + 4 x^3 + 2 x^2\ \text{by} \sqrt{2} x^2\]
Divide 5x3 − 15x2 + 25x by 5x.
Divide 4y2 + 3y +\[\frac{1}{2}\] by 2y + 1.
Divide −21 + 71x − 31x2 − 24x3 by 3 − 8x.
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 |
Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:
3x2 + 4x + 5, x − 2
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.
