Advertisements
Advertisements
प्रश्न
Find whether the first polynomial is a factor of the second.
4 − z, 3z2 − 13z + 4
Advertisements
उत्तर
\[ \frac{{3z}^2 -13z+4}{4-z}\]
\[ = \frac{{3z}^2 -12z-z+4}{4-z}\]
\[ = \frac{3z(z-4)-1(z-4)}{4-z}\]
\[ = \frac{(z-4)(3z-1)}{4-z}\]
\[ = \frac{(4-z)(1-3z)}{4-z}\]
\[ =1-3z \]
\[ \because \text{Remainder = 0}\]
\[ \therefore \text{(4-z) is a factor of}\ {3z}^2 -13z+4.\]
APPEARS IN
संबंधित प्रश्न
Divide the given polynomial by the given monomial.
8(x3y2z2 + x2y3z2 + x2y2z3) ÷ 4x2y2z2
Which of the following expressions are not polynomials?
x2 + 2x−2
Divide 14x2 − 53x + 45 by 7x − 9.
Divide 2y5 + 10y4 + 6y3 + y2 + 5y + 3 by 2y3 + 1.
Divide 6x3 + 11x2 − 39x − 65 by 3x2 + 13x + 13 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 |
Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:
x4 − x3 + 5x, x − 1
Find whether the first polynomial is a factor of the second.
y − 2, 3y3 + 5y2 + 5y + 2
Find whether the first polynomial is a factor of the second.
4x2 − 5, 4x4 + 7x2 + 15
Divide 27y3 by 3y
