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 - 1
1. If two polynomials ax
3
+ 4x
2
+ 3x – 4 and x
3
- 4x + a leave the same remainder when divided by x-3, find
the value of a.
2. Evaluate using identities:
103 * 97
3. Find the remainder when 4x
3
– 3x
2
+2x - 4 is divided by x+2.
4. Show that x - 1 is a factor of x
10
– 1. **
5. Find the value of a, if (x-a) is a factor of x
3
– a
2
x + x + 2.
6. Determine the value of a for which the polynomial 2x
4
– ax
3
+ 4x
2
+ 2x + 1 is divisible by (1-2x). **
7. Factorize: **
(a+b)
3
+ (b+c)
3
+ (c+a)
3
– 3(a+b)(b+c)(c+a)
8. Factorize by splitting the middle term:
a.) x
2
+ 14x + 40
b.) 5x
2
+ 16x + 3
9. If a + b + c = 15 and a
2
+ b
2
+ c
2
= 83, find the value of a
3
+ b
3
+ c
3
– 3abc. **
10. Factorise 8x
6
– x
3
– 9 **
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. 9991
3. -52
4. Proof qn
5. a = -2
6. a = 25
7. 2(a + b + c)(a
3
+ b
3
+ c
3
– ab – bc – ca)
8. a) (x + 4)(x + 10) b) (x + 3)(5x + 1)
9. 180
10. 8y
2
–y – 9 = 8y
2
– 9y + 8y – 9 = (9y + 8) (y – 1)
