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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
Write the degree of each of the following polynomials.
2x + x2 − 8
Which of the following expressions are not polynomials?
Divide 24a3b3 by −8ab.
Divide 72xyz2 by −9xz.
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 |
Find the value of a, if x + 2 is a factor of 4x4 + 2x3 − 3x2 + 8x + 5a.
Divide:
ax2 − ay2 by ax + ay
7ab3 ÷ 14ab = 2b2
Divide: (32y2 – 8yz) by 2y
Statement A: If 24p2q is divided by 3pq, then the quotient is 8p.
Statement B: Simplification of `((5x + 5))/5` is 5x
