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 - 3
1. If f(x) = x
4
– 2x
3
+ 3x
2
– ax + b is a polynomial such that when it is divided by x – 1 and x + 1, the
remainders are 5 and 19 respectively. Determine the remainder when f(x) is divided by (x-2). **
2. Factorize: **
p
3
(q-r)
3
+ q
3
(r-p)
3
+ r
3
(p-q)
3
3. Simplify: **
4. Factorize: **
(x+1)
3
+ (x-1)
3
5. Evaluate using a suitable identity:
(0.07)
3
– (2)
3
+ (1.93)
3
6. Find the value of k if p(x) = kx
3
+ 9x
2
– 10 + 4x leaves the remainder – 22 when divided by (x+3).
7. Factorize by splitting the middle term:
5x
2
+ 16x + 3
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 = 5, b = 8; R = 10
2. 3pqr(p - q)(q - p)(r - p)
3. (a + b)(b + c)(c + a)
4. 2x(x
2
+ 3)
5. 3(-2)(0.07)(1.93) = -0.8106
6. k = 3
7. (5x + 1)(x + 3)
