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 - 5
1. Find the remainder when x
3
– ax
2
+ 6x - a is divided by (x - a).
2. Factorize: i) 6 – x – 2x
2
ii) x
4
+ x
2
+ 1 ii) x
4
+ 4
3. If x
3
+
= 2, find x +
.
4. If the polynomials ax
3
+ 3x
2
- 3 and 2x
3
– 5x + a when divided by x - 4 leave the remainders m and n
respectively and m + n = 0 , find a.
5. Without actually calculating the cubes, find the value of 25
3
– 75
3
+ 50
3
.
6. Find the value of x
3
+ y
3
+ 15xy – 125, if x + y = 5.
7. If (x - 3) and (x -
) are both factors of ax
2
+ 5x + b, then show that a = b.
8. Find the integral zeroes of the polynomial 2x
3
+ 5x
2
– 5x – 2.
9. If the polynomials ax
3
+ 3x
2
– 3 and 2x
3
– 5x + a leave the same remainder when divided by (x – 4), find
a.
10. Find the value of a if (x + 6) is a factor of x
3
+ 3x
2
+ 4x + a.
11. Show that g(x) = x
3
– 3x
2
+ 2x - 6 has only 1 zero.
12. Factorize: i) a
2
+ b
2
+ 2ab + 2bc + 2ca ii) 9x
2
+ 6x + 1 – 25y
2
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. 5a
2. (x+2)(-2x+3) ; (x
2
+ 1 + x)(x
2
+ 1 -x); (x
2
+ 2 – 2x)(x
2
+ 2 + 2x)
3. (x+1/x)
3
= x
3
+ 1/x
3
+ 3(x+1/x)
= 2 + 3(x + 1/x)
Let x + 1/x = z
So, z
3
- 3z - 2 = 0 => (z+1)(z
2
-z -2) = 0 => (z+1)(z+1)(z-2) = 0 => So z = -1, or 2. Or x + 1/x = -1 or 2
4. -153/65
5. -281250
6. 0
7. proof question
8. 1
9. a = 1
10. 132
11. Factorize (x-3)(x
2
+ 2)
12. (a+b)(a+b+2c) ; (3x+1+5y)(3x+1-5y)
