CBSE Class 9 Maths Polynomials MCQs Set 01

Question. In 2 + x + x² the coefficient of x² is:
(a) 2
(b) 1
(c) – 2
(d) –1

Question. In 2 – x² + x³ the coefficient of x² is:
(a) 2
(b) 1
(c) – 2
(d) –1

Question. In πx²/2 +x+10  the coefficient of x² is:
(a)  π/2
(b) 1
(c) – π/2
(d) –1

Question. The degree of 5t – 7 is:
(a) 0
(b) 1
(c) 2
(d) 3

Question. The degree of 4 – y² is:
(a) 0
(b) 1
(c) 2
(d) 3

Question. The degree of 3 is:
(a) 0
(b) 1
(c) 2
(d) 3

Question. The value of p(x) = 5x – 4x² + 3 for x = 0 is:
(a) 3
(b) 2
(c) – 3
(d) – 2

Question. The value of p(x) = 5x – 4x² + 3 for x = – 1 is:
(a) 6
(b) –6
(c) 3
(d) – 3

Question. The value of p(x) = (x – 1)(x + 1) for p(1) is:
(a) 1
(b) 0
(c) 2
(d) – 2

Question. The value of p(t) = 2 + t + 2t² – t³ for p(0) is:
(a) 1
(b) 2
(c) – 1
(d) 3

Question. The value of p(t) = 2 + t + 2t² – t³ for p(2) is
(a) 4
(b) –4
(c) 6
(d) 7

Question. The value of p(y) = y² – y +1 for p(0) is:
(a) –1
(b) 3
(c) –2
(d) 1

Question. (x + 8)(x – 10) in the expanded form is:
(a) x² – 8x – 80
(b) x² – 2x – 80
(c) x² + 2x + 80
(d) x² – 2x + 80

Question. The value of 95 x 96 is:
(a) 9020
(b) 9120
(c) 9320
(d) 9340

Question. The value of 104 x 96 is:
(a) 9984
(b) 9624
(c) 9980
(d) 9986

Question. Without actual calculating the cubes the value of 28³ + (–15)³ +(–13)³ is:
(a) 16380
(b) –16380
(c) 15380
(d) –15380

Question. If x – 2 is a factor of x³ – 2ax² +ax – 1 then the value of a is:
(a) 7/6
(b) –7/6
(c) 6/7
(d) 6/7

Question. If x + 2 is a factor of x³ + 2ax² +ax – 1 then the value of a is:
(a) 2/3
(b) 3/5 
(c) 3/2
(d) 1/2

Question. If x + y + z = 0 then x³ + y³ + z³ is equal to
(a) 3xyz
(b) – 3xyz
(c) xy
(d) –2xy

Question. The factors of 2x² – 7x + 3 are:
(a) (x – 3)(2x – 1)
(b) (x + 3)(2x + 1)
(c) (x – 3)(2x + 1)
(d) (x + 3)(2x – 1)

Question. The factors of 6x² + 5x – 6 are:
(a) (2x – 3)(3x – 2)
(b) (2x – 3)(3x + 2)
(c) (2x + 3)(3x – 2)
(d) (2x + 3)(3x + 2)

Question. The factors of 3x² – x – 4 are:
(a) (3x – 4)(x – 1)
(b) (3x – 4)(x + 1)
(c) (3x + 4)(x – 1)
(d) (3x + 4)(x + 1)

Question. The factors of 12x² – 7x + 1 are:
(a) (4x – 1)(3x – 1)
(b) (4x – 1)(3x + 1)
(c) (4x + 1)(3x – 1)
(d) (4x + 1)(3x + 1)

Question. The factors of x³ – 2x² – x + 2 are:
(a) (x – 1)(x – 1)(x – 5)
(b) (x + 1)(x + 1)(x + 5)
(c) (x + 1)(x – 1)(x + 5)
(d) (x + 1)(x + 1)(x – 5)

Question. Which of the following is not a polynomial?
(a) x² +√2x+3
(b) x²+ √2x+6
(c) x³+3x²+3
(d) 6x+4

Question. The degree of the polynomial 3x³ – x⁴ + 5x + 3 is
(a) –4
(b) 4
(c) 1
(d) 3

Question. Zero of the polynomial p(x) = a²x, a≠0 is
(a) x = 0
(b) x = 1
(c) x = –1
(d) a = 0

Question. Which of the following is a term of a polynomial?
(a) 2x
(b) 3/x
(c) x^√x
(d) x

Question. If p(x) = 5x² – 3x + 7, then p(1) equals
(a) –10
(b) 9
(c) –9
(d) 10

Question. Factorisation of x³ + 1 is
(a) (x + 1)(x² – x + 1)
(b) (x + 1)(x² + x + 1)
(c) (x + 1)(x² – x – 1)
(d) (x + 1)(x² + 1)

Question. If x + y + 2 = 0, then x³ + y³ + 8 equals
(a) (x + y + 2)³
(b) 0
(c) 6xy
(d) –6xy

Question. If x = 2 is a zero of the polynomial 2x² + 3x – p, then the value of p is
(a) –4
(b) 0
(c) 8
(d) 14

Question. x+1/x is
(a) a polynomial of degree 1
(b) a polynomial of degree 2
(c) a polynomial of degree 3
(d) not a polynomial

Question. Integral zeroes of the polynomial (x + 3)(x – 7) are
(a) –3, –7
(b) 3, 7
(c) –3, 7
(d) 3, –7

Question. The remainder when p(x) = 2x² – x – 6 is divided by (x – 2) is
(a) p(– 2)
(b) p(2)
(c) p(3)
(d) p(–3)

Question. If 2(a²+b²)=(a+b)² , then
(a) a + b = 0
(b) a = b
(c) 2a = b
(d) ab = 0

Question. If x³ + 3x² + 3x + 1 is divided by (x + 1), then the remainder is
(a) –8
(b) 0
(c) 8
(d) 1/8

Question. The value of (525)² – (475)² is
(a) 100
(b) 1000
(c) 100000
(d) –100

Question. If a + b = –1, then the value of a³ + b³ – 3ab is
(a) –1
(b) 1
(c) 26
(d) –26

Question. The value of (2 - a)³ + (2 - b)³ + (2 - c)³ - 3(2 - a)(2 - b)(2 - c) when a + b + c = 6 is
(a) –3
(b) 3
(c) 0
(d) –1 

Question. The number of zeroes of the polynomial x³ + x – 3 – 3x² is
(a) 1
(b) 2
(c) 0
(d) 3

Question. If (x + 2) and (x – 2) are factors of ax⁴ + 2x – 3x² + bx – 4, then the value of a + b is
(a) –7
(b) 7
(c) 14
(d) –8

1. A combination of constants and variables connected by +, –, × and ÷ is known as an algebraic expression.
e.g., 2 – 3x + 5x–2 y–1 + 1/3 x/y³

2. An algebraic expression in which the variables involved have only non-negative integral powers is called a polynomial.
e.g., 2 – 3x + 5x²y –1/3 xy³

3. In the case of a polynomial in one variable, the highest power of the variable is called the degree of the polynomial.
e.g., 5x² – 7x + 3/2 is a polynomial in x of degree 3.

4. In the case of polynomials in mor than one variable, the sum of the powers of the variables in each term is taken up and the highest sum so obtained is called the degree of the polynomial.
e.g., 5x³ – 2x²y² – 3x²y + 9y is a polynomial of degree 4 in x and y.

5. A polynomial of degree 1 is called a linear polynomial.

6. A polynomial of degree 2 is called a quadratic polynomial.

7. A polynomial of degree 3 is called a cubic polynomial.

8. A polynomial of degree 4 is called a biquadratic polynomial.

9. A polynomial containing 1 term is called a monomial.

10. A polynomial containing 2 terms is called a bionomial.

11. A polynomial containing 3 terms is called a trinomial.

12. A polynomial containing one term consisting of a constant is called a constant polynomial.

13. The degree of a constant polynomial is zero.

14. The terms of a polynomial are said to be in ascending (or) descending order if they increase (or decrease in degrees respectively.
e.g., (i) 3 – 7x + 5x² – 2x³ is in ascending order
(ii) – 2x³ + 5x² – 7x + 3 is in descending order.

15. Terms with same variables and which have the same exponents are called like or similar terms, otherwise they are called unlike (or) dissimilar terms.
e.g., (i) 3x³, 1/2x³ , – 9x³, ....etc, are like terms.
(ii) x²y, 3xy², – 4x³, ... etc are unlike terms.

16. Dividend = (divisor × quotient) + reminder.

Question. If (x–2) is one factor of x² + ax – 6 = 0 and x² – 9x + b = 0 then a+b =
(A) 15
(B) 13
(C) 11
(D) 10

Answer: A

Question. The remainder obtained when t6 + 3t² + 10 is divided by t³ + 1 is
(A) t² – 11
(B) t³ – 1
(C) 3t² + 11
(D) none

Answer: C

Question. The value of the product (3x² – 5x + 6) and (–8x³) when x = 0 is
(A) ½
(B) 2
(C) 1
(D) 0

Answer: D

Question. The difference of the degrees of the polynomials 3x²y³ + 5xy⁷ – x⁶ and 3x⁵ – 4x³ + 2 is
(A) 2
(B) 3
(C) 1
(D) none

Answer: B

Question. What must be added to x² + 5x – 6 to get x³ – x² + 3x – 2?
(A) x³ – x² + 3x – 2
(B) x³ – 2x² – 2x – 4
(C) x³ – 2x – 2x + 4
(D) none

Answer: C

Question. What must be subtracted from x⁴ + 2x² – 3x + 7 to get x³ + x² + x – 1?
(A) x⁴ – x³ + x² – 4x + 8
(B) x³ + x² – 4x + 8
(C) x⁴ – x³ + x² + 4x – 8
(D) x⁴ – x³ – x² + 4x – 8

Answer: A