LOTUS VALLEY INTERNATIONAL SCHOOL
SECTOR - 126 EXPRESSWAY, NOIDA
CLASS - IX
SUBJECT: MATHS
CH- POLYNOMIALS
Objective Type Questions
1. The degree of a polynomial is the _____
(i) largest coefficient of x (ii) smallest coefficient of x
(iii) highest power of x (iv) lowest power of x
2. When 9x2 − 6x + 2 is divided by x − 3, the value will be
(i) 60 (ii) 65 (iii) 15 (iv) 25
3. When x − 16x + 30, is divided by x − 15 the value of the resulting polynomial is
2
(i) 30 (ii) 14 (iii) 15 (iv) 16
4. If (x − 3) is a factor of x3 − (2+k)x2 + 7k, then k =
(i) 4 (ii) 4.5 (iii) 5 (iv) 5.5
5. Find the value when x3 + 9x + 5 is divided by x
(i) 9 (ii) -9 (iii) 5 (iv) 0
6. If (x −1) is a factor of ax + a, then the value of a is
(i) 0 (ii) 2 (iii) 3 (iv) any real number
7. If f(x) is x2 − 3x + 2 is a polynomial, then f(2) =
(i) 1 (ii) 0 (iii) 2 (iv) none of these
8. Which one is not a polynomial
3
(i) 4x2 + 2x – 1 (ii) y + (iii) x3 – 1 (iv) y2 + 5y + 1
y
9. The zero of the polynomial p(x) = 2x + 5 is
2 −5
(i) 2 (ii) 5 (iii) (iv)
5 2
10. The value of
(i) 300 (ii) 500 (iii) 400 (iv) 600
11. Degree of the polynomial f(x) = 4x4 + 0x3 + 0x5 + 5x + 7 is
(a) 0 (ii) 4 (iii) 3 (iv) 5
12. √2 is a polynomial of degree
(a) 0 (ii) 4 (iii) 3 (iv) 5
13. If f(x) = x + 3, then f(x) + f(–x) is equal to
(a) 3 (ii) 2x (iii) 0 (iv) 6
14. If f (x) = 2 - 2√2x + 1, then f (2√2) is equal to
(a) 1 (ii) 4√2 (iii) 0 (iv) 8√2 + 1
15. x + 1 is a factor of the polynomial
(a) x3 + x2 – x + 1
(b) x3 + x2 + x + 1
(c) x4 + x3 + x2 + 1
(d) x4 + 3x3 + 3x2 + x + 1
16. If x2 + kx + 6 = (x + 2) (x + 3) for all x, then the value of k is
(a) 3 (ii) 1 (iii) -1 (iv) 5
17. If x − 2 is a factor of x2 + 3ax − 2a, then a =
(a) 2 (ii) 1 (iii) -1 (iv) -2
18. If x3 + 6x2 + 4x + k is exactly divisible by x + 2, then k =
(a) -10 (ii) -8 (iii) -7 (iv) -6
19. If x140 + 2x151 + k is divisible by x + 1, then the value of k is
(a) - 3 (ii) 2 (iii) - 1 (iv) - 2
20. If x51 + 51 is divided by x + 1, the remainder is
(a) 0 (ii) 1 (iii) 49 (iv) 50
Subjective Type Questions
1. If y = -1 is a zero of the polynomial q (y) = 4y3 + ky2 - y -1, then find the value of k
2. For what value of m is x3 – 2mx2 + 16 divisible by (x + 2)
3. If a + b + c = 9 and ab + bc + ca = 26, find a2 + b2 + c2
4. Find the value of (a) when (x – 1) is a factor of polynomial p(x) = 2x3 + 3x2 – ax + 9
101
5. Find the value when (x – 1) is divided by(x - 1)
6. Factorise
i) 2x2 + 9y2 + 16 + 6√2xy - 24yz - 8√2xz
ii) 8x3 + 60x2 + 150x + 125
4 3
7. If (x - 2a) is a factor of 2x - 4ax + 7x2 - 13ax - 18, find the value of a.
8. Factorise the given expression: 9x2 + 49y2 + 25z2 - 42xy - 30xz + 70yz
9. If both (x+1) and (x-1) are the factors of (ax3 + x2 - 2x + b), find a and b
10. Find the value when the polynomial p(x) = (12x3 - 13x2 - 5x + 7) is divided by g(x) = (2+3x)
11. If f (x) = 2x3 – 13x2 + 17x + 12, find
(i) f (2) (ii) f (-3) (iii) f (0)
12. Factorise
(i) a3 - 2√2b3 (ii) x2 - 1 -2a - a2 (iii) a3 + b3 + a + b
(iv) 3(x+2)2 – 5(x+2) + 2 (v) x6 + y6 (vi) 3√3x3 – 5√5y3
3 3
(vii) 125x - 64y
13. Find the value when 3x3 + x2 - 22x + 9 is divided by x-3
14. Simplify :
(i) (x+y)3 - (x-y)3
15. Find the value of
i) ( 36 )3 + ( -20 )3 + ( -16 )3
ii) ( -14 )3 + ( 10 )3 + ( 4 )3
16. Show that :-
(1) (a-1)(b-c) + (b-1)(c-a) + (c-1)(a-b) = 0
(2) (p-1)(q-r) + (q-1)(r-p) + (r-1)(p-q) = 0
(3) (x-1)(y-z) + (y-1)(z-x) + (z-1)(x-y) = 0
17. Find the value of (a) if (x - 2) is a factor of p(x) x3 + 3x2 - ax + 3.
18. Factorise :
(i) x3 – 6x2 – 19x + 84 (ii) x3 + 6x2 + 11x + 6
(iii) x3 – 6x2 + 3x + 10 (iv) y3 – 7y + 6
19. Find the value when 2x3 - 9x2 + x + 12 when divided by x - 1
20. Find the value of a, if (x + a) is a factor of x3 + ax2 - 2x + a + 4
21. Show that (x – 1) (x – 10) (x – 12) are factors of x3 – 23x2 – 142x – 120
22. If ( x − 2) is a factor of the polynomial 2x2 + ax + 12 and (x − 3) is a factor of the polynomial
3 2
x − 7x + 11 x + b , then what is the value of (2a + b)?
3 3 3
23. If a + b + c = 8 and ab + bc + ca = 20, find the value of a + b + c - 3abc
24. Evaluate each of the following using identities:
2 2.
(i) (399) (ii) (0.98) (iii) 991 x 1009
(iv) 117 x 83 (v) (3x + 4y)3 (vi) (2a − 3b)
25. Factorise each of the following :
(i) x3 + 125 (ii) x3 − 0.027 (iii) x8 - y8
2 2 2 2 2 2 2 2 2
(iv) ab (a + b − c ) + bc (a + b − c ) − ca (a + b − c )
ASSERTION AND REASONING
DIRECTION : In each of the following questions, a statement of Assertion is given followed by
a corresponding statement of Reason just below it. Of the statements, mark the correct answer as
(a) Both assertion and reason are true and reason is the correct explanation of assertion.
(b) Both assertion and reason are true but reason is not the correct explanation of assertion.
(c) Assertion is true but reason is false.
(d) Assertion is false but reason is true.
Q1. Assertion : If P(x)= -3x7 + ax2 + bx + 6 is a polynomial, then its degree is 7.
Reason : Degree of a polynomial is the highest power of the variable in it.
Now mark the correct answer as
(a) Both assertion and reason are true and reason is the correct explanation of assertion.
(b) Both assertion and reason are true but reason is not the correct explanation of assertion.
(c) Assertion is true but reason is false. (d) Assertion is false but reason is true.
Q2. Assertion : The degree of the polynomial (x-2)(x-3)(x-4) is 4.
Reason : The number of zeroes of a polynomial is the degree of that polynomial.
Now mark the correct answer as
(a) Both assertion and reason are true and reason is the correct explanation of assertion.
(b) Both assertion and reason are true but reason is not the correct explanation of assertion.
(c) Assertion is true but reason is false.
(d) Assertion is false but reason is true.
Q3. Assertion : The expression 3x4 -4x3/2 + x + 6 =2 is not a polynomial because the term
-4x3/2 contains a rational power of x .
Reason : The highest exponent in various terms of an algebraic expression in one variable is
called its degree.
Now mark the correct answer as
(a) Both assertion and reason are true and reason is the correct explanation of assertion.
(b) Both assertion and reason are true but reason is not the correct explanation of assertion.
(c) Assertion is true but reason is false.
(d) Assertion is false but reason is true.
