CLASS IX
CHAPTER 2: POLYNOMIALS
1. Which of the following expressions are not polynomials in one variable?
Give reasons in support of your answer.
i.
+√2
ii.
² + +5
iii.
7+3y
iv.
¼+
²
2. For what value of k, x=4 is a zero of the polynomial 2 -3x²-18x+k?
3. Find the remainder and quotient when
i. +1 is divided by x+1.
ii. ³-3x²+5x+11 is divided by x-2.
4. Find the value of k, if the polynomial p(x)= 4x³-12x²+14x-k when divided by
2x-1 leaves remainder .
5. Find the zeros of the following polynomials:
i. p(x)= x²-16
ii. p(x)= 4x²-4x+1
iii. p(x)= rx+q, r≠0
iv. p(x)= 3x²-7x+4
6. Check whether g(x) = 2x³+5x²+3x+2 is a factor of g(x) = x+2.
7. Use appropriate identity to find the following products:
i. (2x+1) (2x+1)
ii. (3x+4)(3x-5)
iii. (4x-1)(4x+1)
iv.
( x+1)³
v. (4m-7n)(16m²+28mn+49n²)
vi. (2x-3y+7z)²
8. Evaluate using appropriate identity:
i. (99)³
ii. (102)²
iii. 91×109
9. The polynomials ax³+3x²-13 and 2x³-5x+a are divided by(x+3). If the
remainder in each case is same, find the value of a.
10.If the polynomial p(x) = 6x³+2x²-ax+b, when divided by (x+1) leaves
remainder 14 and (x-1) is a factor of p(x). Find b and a.
11.Factorize the following:
i. 16x²+32x+15
ii. 9x²-3x-2
iii. x³-23x²+142x-120
iv. 2y³+y²-2y-1
v. x³+6x²+12x+8
vi.
x²-
²
vii.
-625
viii.
2² + ² + 8² − 2√2 + 4√2 − 8
ix.
27p³-
- ² + x. 8+x³
xi. (2a+b)³+ (2a-b)³
xii. p³-27q³+8r³+18pqr
12.If x+ y +z=0, show that x³+y³+z³=3xyz.
13.Verify that:
X³+y³+z³- 3xyz= (x+y+z) [(x-y) ²+(y-z) ²+ (z-x) ²]
14.Evaluate the following using suitable identity:
(11)³+ (14)³-(25)³
15.Consider the polynomial p(x) =0. Then degree of p(x) is
a) 0
b) 1
c) 2
d) none of these