Advertisements
Advertisements
प्रश्न
Find whether the first polynomial is a factor of the second.
4 − z, 3z2 − 13z + 4
Advertisements
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 each of the following polynomials in the standard form. Also, write their degree.
a2 + 4 + 5a6
Divide 72xyz2 by −9xz.
Divide x + 2x2 + 3x4 − x5 by 2x.
Divide 5x3 − 15x2 + 25x by 5x.
Divide 3x3 + 4x2 + 5x + 18 by x + 2.
Divide m3 − 14m2 + 37m − 26 by m2 − 12m +13.
Divide 14x3 − 5x2 + 9x − 1 by 2x − 1 and find the quotient and remainder
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 |
Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.
| Dividend | Divisor |
| 6y5 + 4y4 + 4y3 + 7y2 + 27y + 6 | 2y3 + 1 |
Using division of polynomials, state whether
z2 + 3 is a factor of z5 − 9z
