2. Check in which case the first polynomial is a factor of the second polynomial by dividing
the second polynomial by the first polynomial :
(i) t2
– 3, 2t
4
+ 3t
3
– 2t
2
– 9t – 12
(ii) x
2 + 3x + 1, 3x
4
+ 5x
3
– 7x
2
+ 2x + 2
(iii) x
3
– 3x + 1, x
5
– 4x
3
+ x
2
+ 3x + 1
3. Obtain all other zeroes of 3x
4
+ 6x
3
– 2x
2
– 10x – 5, if two of its zeroes are
√5/3
and - √
5/
3
4. On dividing x
3
– 3x
2
+ x + 2 by a polynomial g(x), the quotient and remainder were
x – 2 and – 2x + 4, respectively. Find g(x).
5. Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm
and
(i) deg p(x) = deg q(x)
(ii) deg q(x) = deg r(x)
(iii) deg r(x) = 0
OPTIONAL EXERCISE
[For extensive learning]
1. Verify that the numbers given alongside the cubic polynomials below are their zeroes.
Also verify
3
+ x
2
– 5x + 2 ; (
1/
2
, 1, –2)
(ii) x3
+ 4x
2
+ 5x – 2 ; (1, 1, 1)
2. Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a
time, and the product of its zeroes as 2, –7, –14 respectively.
3. If the zeroes of the polynomial x
3
– 3x
2
+ x + 1 are a – b, a, a + b find a and b.
4. If two zeroes of the polynomial x
4 – 6x
3
– 26x
2
+ 138x – 35 are 2 ± √3 , find the other
zeroes.
5. If the polynomial x
4 – 6x
3
– 16x
2
+ 25x + 10 is divided by another polynomial