NEW LEARNET EDUCATION
Chapter 2 Polynomials ( HANDWRITTEN MCQ )
PART - 1
1) x2-2x+1 is a polynomial in:
a. One Variable
b. Two Variables
c. Three variable
d. None of the above
Answer: a
Explanation: x2-2x+1 can be written as x2-2x1+1x0. Hence, we can see that x is the only variable having powers as whole numbers: 2,1 and 0.
2) The coefficient of x2 in 3x3+2x2-x+1 is:
a. 1
b. 2
c. 3
d. -1
Answer: b
Explanation: The coefficient of x2 in equation 3x3+2x2-x+1 is the multiple of x2.
3) A binomial of degree 20 in the following is:
a. 20x + 1
b. x/20 + 1
c. x20 +1
d. x2+20
Answer: c
Explanation: A polynomial having two terms and the highest degree 20 is called a binomial of degree 20.
4) The degree of 4x3-12x2+3x+9 is
a. 0
b. 1
c. 2
d. 3
Answer: d
Explanation: The degree is the highest power of a variable in an equation.
5) x2 – x is ________ polynomial.
a. Linear
b. Quadratic
c. Cubic
d. None of the above
Answer: b
Explanation: A polynomial of degree two is known as a quadratic polynomial.
6) x – x3 is a ________ polynomial.
a. Linear
b. Quadratic
c. Cubic
d. None of the above
Answer: c
Explanation: A polynomial of degree three is known as a cubic polynomial.
7) 1+3x is a _________ polynomial.
a. Linear
b. Quadratic
c. Cubic
d. None of the above
Answer: a
Explanation: A polynomial of degree one is known as a linear polynomial.
8) The value of f(x) = 5x−4x2+3 when x = -1, is:
a. 3
b. -12
c. -6
d. 6
Answer: c
Explanation: When x= -1
f(x)=5x−4x2+3
f(−1)=5(−1) −4(−1)2+3
=−5–4+3
=−6
9) The value of p(t) = 2+t+2t2−t3 when t=0 is
a. 2
b. 1
c. 4
d. 0
Answer: a
Explanation: p(0)=2+0+2(0)2–(0)3=2
10) The zero of the polynomial f(x) = 2x+7 is
a. 2/7
b. -2/7
c. 7/2
d. -7/2
Answer: d
Explanation: f(x)=2x+7
⇒2x+7=0
⇒2x=−7
⇒x=−7/2
∴x = −7/2 is a zero polynomial of the polynomial f(x).
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PART - 2
Question 1.
Find the product of (x – 1x) (x + 1x) (x² + 1x2)
(a) x4 + 1x4
(b) x³ + 1x3 – 2
(c) x4 – 1x4
(d) x² + 1x2 + 2
Answer
Answer: (c) x4 – 1x4
Question 2.
If xy + yx = -1 (x, y ≠ 0), then find the value of x³ – y³
(a) 1
(b) -1
(c) 12
(d) 0
Answer
Answer: (d) 0
Question 3.
Find the value of 525² – 475².
(a) 100
(b) 10000
(c) 50000
(d) 100000
Answer
Answer: (c) 50000
Question 4.
One of the factors of (1 + 3y)² + (9y² – 1) is
(a) 1 – 3y
(b) 3 – y
(c) 3y + 1
(d) y – 3
Answer
Answer: (c) 3y + 1
Question 5.
One of the factors of (x³ – 1) – (x – 1) is
(a) x² + 1
(b) x² – 1
(c) x – 1
(d) x + 4
Answer
Answer: (c) x – 1
Question 6.
Find the degree of polynomial √2 .
(a) 2
(b) 0
(c) 1
(d) 12
Answer
Answer: (b) 0
Question 7.
Find the value of k if x² + kx + 6 = (x + 2) (x + 3) for all k.
(a) 1
(b) -1
(c) 5
(d) 3
Answer
Answer: (c) 5
Question 8.
If x – 2 is a factor of 5x² – kx – 18, then find the value of k.
(a) -1
(b) 1
(c) 0
(d) 5
Answer
Answer: (b) 1
Question 9.
Find the coefficient of x² in (3x² – 5) (4 + 4x²).
(a) 12
(b) 5
(c) -8
(d) 8
Answer
Answer: (c) -8
Question 10.
Find the value of p for which x + p is a factor of x² + px + 3 – p.
(a) 1
(b) -1
(c) 3
(d) -3
Answer
Answer: (c) 3
Question 11.
Zero of the polynomial p(x) = cx + d is
(a) -d
(b) -c
(c) dc
(d) –dc
Answer
Answer: (d) –dc
Question 12.
Find the remainder on dividing 5y³ – 2y² – 7y + 1 by y.
(a) -1
(b) 1
(c) 0
(d) 2
Answer
Answer: (b) 1
Question 13.
One of the factors of (16y² – 1) + (1 – 4y)²
(a) (4 + a)
(b) (4 – y)
(c) (4y + 1)
(d) 8y
Answer
Answer: (d) 8y
Question 14.
If a + b + c = 0, then the value of a³ + b³ + c³
(a) abc
(b) -3abc
(c) 0
(d) 3abc
Answer
Answer: (d) 3abc
Question 15.
If x13 + y13 + z13 = 0, then which one of the expression is correct.
(a) x³ + y³ + z³ = 0
(b) x + y + z = 3x13y13z13
(c) x + y + z = 3xyz
(d) x³ + y³ + z³ = 3xyz
Answer
Answer: (b) x + y + z = 3x13y13z13
Question 16.
If the area of the rectangle is 4x² + 4x – 3, then find its possible dimensions.
(a) 2x – 3, 2x + 1
(b) 2x – 1, 2x + 3
(c) 3x + 1, 2x – 3
(d) 3x – 1, 2x + 3
Answer
Answer: (b) 2x – 1, 2x + 3
Question 17.
If x + 1x = 4, then the value of x² + 1x2
(a) 8
(b) 14
(c) 16
(d) 20
Answer
Answer: (b) 14
Question 18.
For what value of b, is the polynomial x³ – 3x² + bx – 6 divisible by x – 3?
(a) 1
(b) 2
(c) 3
(d) -3
Answer
Answer: (b) 2
Question 19.
When p(x) is divided by ax – b, then the remainder is
(a) p(a + b)
(b) P(−ba)
(c) p(ab)
(d) p(ba)
Answer
Answer: (d) p(ba)
Question 20.
What is remainder when x³ – 2x² + x + 1 is divided by x – 1?
(a) 0
(b) -1
(c) 1
(d) 2
Answer
Answer: (c) 1
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PART -3
1) x2-2x+1 is a polynomial in:
a. One Variable
b. Two Variables
c. Three variable
d. None of the above
Answer/Explanation
Answer: (a)
Explanation: x2-2x+1 can be written as x2-2x1+1x0. Hence, we can see that x is the only variable having powers as whole numbers: 2,1 and 0.
2) The coefficient of x2 in 3x3+2x2-x+1 is:
a. 1
b. 2
c. 3
d. -1
Answer/Explanation
Answer: (b)
Explanation: The coefficient of x2 in equation 3x3+2x2-x+1 is the multiple of x2.
3) A binomial of degree 20 in the following is:
a. 20x + 1
b. x/20 + 1
c. x20 +1
d. x2+20
Answer/Explanation
Answer: (c)
Explanation: A polynomial having two terms and the highest degree 20 is called a binomial of degree 20.
4) The degree of 4x3-12x2+3x+9 is
a. 0
b. 1
c. 2
d. 3
Answer/Explanation
Answer: (d)
Explanation: The degree is the highest power of a variable in an equation.
5) x2 – x is ________ polynomial.
a. Linear
b. Quadratic
c. Cubic
d. None of the above
Answer/Explanation
Answer: (b)
Explanation: A polynomial of degree two is known as quadratic polynomial.
6) x – x3 is a ________ polynomial.
a. Linear
b. Quadratic
c. Cubic
d. None of the above
Answer/Explanation
Answer: (c)
Explanation: A polynomial of degree three is known as cubic polynomial.
7) 1+3x is a _________ polynomial.
a. Linear
b. Quadratic
c. Cubic
d. None of the above
Answer/Explanation
Answer: (a)
Explanation: A polynomial of degree one is known as linear polynomial.
8) The value of f(x) = 5x−4x2+3 when x = -1, is:
a. 3
b. -12
c. -6
d. 6
Answer/Explanation
Answer: (c)
Explanation: When x= -1
f(x)=5x−4x2+3
f(−1)=5(−1) −4(−1)2+3
=−5–4+3
=−6
9) The value of p(t) = 2+t+2t2−t3 when t=0 is
a. 2
b. 1
c. 4
d. 0
Answer/Explanation
Answer: (a)
Explanation: p(0)=2+0+2(0)2–(0)3=2
10) The zero of the polynomial f(x) = 2x+7 is
a. 2/7
b. -2/7
c. 7/2
d. -7/2
Answer/Explanation
Answer: (d)
Explanation: f(x)=2x+7
⇒2x+7=0
⇒2x=−7
⇒x=−7/2
∴x = −7/2 is a zero polynomial of the polynomial f(x).
11) A polynomial with one degree is called:
a) Linear polynomial
b) Quadratic polynomial
c) Monomial
d) Binomial
Answer
(b)
12) √3 is a polynomial of degree:
a) 2
b) 0
c) 1
d) 1/2
Answer
(b)
13) Degree of the polynomial 7x5 + 8x2 – 5x + 3 is:
a) 1
b) 3
c) 2
d) 5
Answer
(d)
14) What is the degree of a zero polynomial?
a) 0
b) 1
c) Any natural number
d) Not defined
Answer
(d)
15) The value of the polynomial 7x4 + 3x2 – 4, when x = – 2 is:
a) 100
b) 110
c) 120
d) 130
Answer
(c)
16) The zero of the polynomial p(x) = -9x + 9is:
a) 0
b) -9
c) -1
d) 1
Answer
(d)
17) √12 X √15 is equal to:
a) 5√6
b) 6√5
c) 10√5
d) √25
Answer
(b)
18) If y97 + 97 is divided by y + 1, the remainder is:
a) 0
b) 1
c) 95
d) 96
Answer
(d)
19) If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is:
a) -3
b) 4
c) 2
d) -2
Answer
(c)
20) The value of 992 – 982 is:
a) 1
b) 197
c) 187
d) 207
Answer
(b)
21) One of the factors of (1 + 7x)2 + (49x2 – 1) is:
a) x – 7
b) 7 – x
c) 7x – 1
d) 14x
Answer
(d)
22) The factorization of 6x2 + 11x + 3 is:
a) (3x + 1) (2x + 3)
b) (x + 1) (2x + 3)
c) (x + 3) (2x + 1)
d) (3x + 3) (x + 1)
Answer
(a)
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