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प्रश्न
Find whether the first polynomial is a factor of the second.
4x2 − 5, 4x4 + 7x2 + 15
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उत्तर
\[(\frac{4 x^4 +^2 +15}{{4x}^2 -5}\]
\[ = \frac{x^2 {(4x}^2 {-5)+3(4x}^2 -5)+30}{{4x}^2 -5}\]
\[ = \frac{( {4x}^2 {-5)(x}^2 +3 ) +30}{{4x}^2 -5}\]
\[ {=(x}^2 +3 ) + \frac{30}{{4x}^2 -5}\]
\[ \because \text{Remainder = 30}\]
\[\text{Therefore,} (4 x^2 - 5) \text{is not a factor of}\ 4 x^4 + 7 x^2 + 15\]
संबंधित प्रश्न
Divide the given polynomial by the given monomial.
(x3 + 2x2 + 3x) ÷ 2x
Write each of the following polynomials in the standard form. Also, write their degree.
x2 + 3 + 6x + 5x4
Divide 9x2y − 6xy + 12xy2 by −\[\frac{3}{2}\]
Divide x2 + 7x + 12 by x + 4.
Divide x4 − 2x3 + 2x2 + x + 4 by x2 + x + 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
2y − 5 is a factor of 4y4 − 10y3 − 10y2 + 30y − 15
Using division of polynomials, state whether
3y2 + 5 is a factor of 6y5 + 15y4 + 16y3 + 4y2 + 10y − 35
Using division of polynomials, state whether
2x2 − x + 3 is a factor of 6x5 − x4 + 4x3 − 5x2 − x − 15
Statement A: If 24p2q is divided by 3pq, then the quotient is 8p.
Statement B: Simplification of `((5x + 5))/5` is 5x
