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प्रश्न
Find whether the first polynomial is a factor of the second.
4 − z, 3z2 − 13z + 4
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उत्तर
\[ \frac{{3z}^2 -13z+4}{4-z}\]
\[ = \frac{{3z}^2 -12z-z+4}{4-z}\]
\[ = \frac{3z(z-4)-1(z-4)}{4-z}\]
\[ = \frac{(z-4)(3z-1)}{4-z}\]
\[ = \frac{(4-z)(1-3z)}{4-z}\]
\[ =1-3z \]
\[ \because \text{Remainder = 0}\]
\[ \therefore \text{(4-z) is a factor of}\ {3z}^2 -13z+4.\]
संबंधित प्रश्न
Divide the given polynomial by the given monomial.
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Divide the given polynomial by the given monomial.
(x3 + 2x2 + 3x) ÷ 2x
Divide 6x3y2z2 by 3x2yz.
Divide x + 2x2 + 3x4 − x5 by 2x.
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
3y2 + 5 is a factor of 6y5 + 15y4 + 16y3 + 4y2 + 10y − 35
Find whether the first polynomial is a factor of the second.
y − 2, 3y3 + 5y2 + 5y + 2
Divide:
acx2 + (bc + ad)x + bd by (ax + b)
Statement A: If 24p2q is divided by 3pq, then the quotient is 8p.
Statement B: Simplification of `((5x + 5))/5` is 5x
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.
