Advertisements
Advertisements
Question
Divide\[- x^6 + 2 x^4 + 4 x^3 + 2 x^2\ \text{by} \sqrt{2} x^2\]
Solution
\[\frac{- x^6 + 2 x^4 + 4 x^3 + 2 x^2}{\sqrt{2} x^2}\]
\[ = \frac{- x^6}{\sqrt{2} x^2} + \frac{2 x^4}{\sqrt{2} x^2} + \frac{4 x^3}{\sqrt{2} x^2} + \frac{2 x^2}{\sqrt{2} x^2}\]
\[ = \frac{- 1}{\sqrt{2}} x^{(6 - 2)} + \sqrt{2} x^{(4 - 2)} + 2\sqrt{2} x^{(3 - 2)} + \sqrt{2} x^{(2 - 2)} \]
\[ = \frac{- 1}{\sqrt{2}} x^4 + \sqrt{2} x^2 + 2\sqrt{2}x + \sqrt{2}\]
APPEARS IN
RELATED QUESTIONS
Write the degree of each of the following polynomials.
Write each of the following polynomials in the standard form. Also, write their degree.
x2 + 3 + 6x + 5x4
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 |
| 4y3 + 8y + 8y2 + 7 | 2y2 − y + 1 |
Divide 15y4 + 16y3 +\[\frac{10}{3}\]y − 9y2 − 6 by 3y − 2. Write down the coefficients of the terms in the quotient.
Using division of polynomials, state whether
4x − 1 is a factor of 4x2 − 13x − 12
Using division of polynomials, state whether
3y2 + 5 is a factor of 6y5 + 15y4 + 16y3 + 4y2 + 10y − 35
What must be added to x4 + 2x3 − 2x2 + x − 1 , so that the resulting polynomial is exactly divisible by x2 + 2x − 3?
Find whether the first polynomial is a factor of the second.
y − 2, 3y3 + 5y2 + 5y + 2
Divide:
(a2 + 2ab + b2) − (a2 + 2ac + c2) by 2a + b + c
