Hg
Name: Class 9 Date:
___________________________________________________________________________________________________________________________________
___________________________________________________________________________________________________________________________________
The Hg Classes (8
th
to 12
th
) By: Er Hershit Goyal (B.Tech. IIT BHU), 134-SF, Woodstock Floors, Nirvana Country, Sector 50, GURUGRAM +91 9599697178.
fb.me/thehgclasses linkedin.com/company/the-hg-classes instagram.com/the_hg_classes g.page/the-hg-classes-gurugram thehgclasses.co.in
Polynomials - 2
1. If two polynomials (3x
3
+ ax
2
+ 3x + 5) and (4x
3
+ x
2
-2x + a) leave the same remainder when divided by
(x-2) then find the value of a. **
2. Factorize using identities: a
3
– 0.216
3. Factorize 2x
4
+ x
3
– 14x
2
– 19x – 6. **
4. Find the value of k if p(x) = kx
3
+ 9x
2
– 10 + 4x leaves the remainder – 22 when divided by (x+3).
5. Without actually calculating the cubes find the value of (-32)
3
+ 27
3
+ 5
3
.
6. If x = 2y + 6, then find the value of x
3
– 8y
3
– 36xy – 216. **
[Hint: Cube both sides of (x-2y)=6 and use identity (a-b)
3
]
7. If x
2
-1 is a factor of ax
4
+ bx
3
+ cx
2
+ dx + e, the prove that a + c + e = b + d = 0. **
8. If f(x) = x
3
+ px
2
+ qx + 6 leaves remainder 3 when divided by (x-3), and leaves remainder zero when
divided by (x-2), find the value of p and q. **
9. The polynomial p(x) = k + 3x
3
+ 6 when divided by (x-2) leaves remainder which is double the remainder
left by the polynomial g(x) = 2x
3
+ 17x + k when divided by (x-2), find the value of k.
Hg
Name: Class 9 Date:
___________________________________________________________________________________________________________________________________
___________________________________________________________________________________________________________________________________
The Hg Classes (8
th
to 12
th
) By: Er Hershit Goyal (B.Tech. IIT BHU), 134-SF, Woodstock Floors, Nirvana Country, Sector 50, GURUGRAM +91 9599697178.
fb.me/thehgclasses linkedin.com/company/the-hg-classes instagram.com/the_hg_classes g.page/the-hg-classes-gurugram thehgclasses.co.in
Answers:
1. a = -1
2. (a – 0.6)(a
2
+ 0.6a + 0.36)
3. (x + 1)(x + 2)(x - 3)(2x + 1)
4. k = 3
5. -12,960
6. 0
7. Proof qn.
8. p = -17/5, q = 1/5
9. k = -70
