Polynomials Test

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Polynomials Test - 15

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following is a monomial with only y as a variable?

A
3y + 3y²

B
3xy

C
3y

D
3y + x

Solution

A monomial is an expression with only one term.
So, 3y is a monomial with only y as a variable.
Question 2
1 / -0

What will you get on subtracting ab + bc + ca from 2ab – 2bc + 3?

A
3ab + 3bc + ca + 3

B
– ab – bc – ca + 3

C
ab – 3bc – ca + 3

D
ab – 3bc + ca + 3

Solution
Question 3
1 / -0

What is the value of (2x + y)(2x - y) + (y + 2z)(y - 2z) + (2z + 2x)(2z - 2x)?

A
1

B
0

C
(y + x)

D
(y - x)z

Solution

(2x + y)(2x - y) + (y + 2z)(y - 2z) + (2z + 2x)(2z - 2x)
= (4x² - y²) + (y² - 4z²) + (4z² - 4x²) [ (a + b) (a - b) = a² - b²]
= 4x² - y² + y² - 4z² + 4z² - 4x²
= 0
Question 4
1 / -0

If (2m + 3n) = 2 and mn = – 1, what is the value of 4m² + 9n²?

A
– 8

B
8

C
16

D
– 16

Solution

2m + 3n = 2
Squaring both sides, we get
(2m + 3n)² = 4
We know that (a + b)² = a² + b² + 2ab.
So, the above equation becomes: 4m² + 9n² + 12mn = 4
Or 4m² + 9n² – 12 = 4
Or 4m² + 9n² = 4 + 12
Or 4m² + 9n² = 16

Hence, (3) is the correct option.
Question 5
1 / -0

What will you get when you subtract 2p²q + 4p - 2q from 2p + 4q + 2q²p?

A
6p + 2q + 2pq² + 2p²q

B
2p - 2q - 2pq² + 2p²q

C
-2p + 6q

D
-2p + 6q + 2pq² - 2p²q

Solution
Question 6
1 / -0

Which of the following is one of the factors of a⁴ – b⁴?

A
(2a – b)

B
(a² + b²)

C
(a² – b³)

D
(a³+ b²)

Solution

a⁴ – b⁴ = (a²)² – (b²)² [ a² – b² = (a + b) (a – b)]
= (a² + b²)(a² – b²)
= (a² + b²)(a + b)(a – b)
So, (a² + b²) is one of the factors of a⁴ – b⁴ .

Hence, (2) is the correct option.
Question 7
1 / -0

What is the result of (2x + y)² + (2x - y)²?

A
2(4x² + y²)

B
2(4x² + y² + 4xy)

C
8xy

D
8xy + y² + x²

Solution

(2x + y)² + (2x - y)² ... (1)
We know,
(a + b)² = a² + b² + 2ab
(a - b)² = a² + b² - 2ab
Expression (1) becomes as follows:
4x² + y² + 4xy + 4x² + y² - 4xy
= 8x² + 2y²
= 2(4x² + y²)
Hence, (1) is the correct option.
Question 8
1 / -0

If x + y = 3 and xy = 2, what is the value of x² + y²?

A
4

B
5

C
6

D
8

Solution

x + y = 3
Squaring both sides, we get
(x + y)² = 9
x² + y² + 2xy = 9
Or x²+ y² = 9 – 2(2)
= 9 – 4
= 5
Question 9
1 / -0

What is the simplified form of [5 - 3x + 2y - (2x - y)] - (3x - 7y + 9)?

A
-4 - 8x + 10y

B
-4 - 4x + 10y

C
-4(1 - x + y)

D
-4(1 - 2x + 2y)

Solution

[5 - 3x + 2y - (2x - y)] - (3x - 7y + 9)
5 - 3x + 2y - 2x + y - 3x + 7y - 9
= -8x + 10y - 4
Hence, (1) is the correct option.
Question 10
1 / -0

What is the value of a(a² + a + 1) + 5 for a = 0?

A
0

B
1

C
5

D
6

Solution

a(a² + a + 1) + 5
Putting a = 0, we get
0(0² + 0 + 1) + 5
= 0(1) + 5 = 0(1) + 5
= 5
Question 11
1 / -0

If x + y = 4 and xy = 2, then what is the value of x² + y²?

A
18

B
16

C
12

D
8

Solution

x + y = 4 and xy = 2
(x + y)² = x² + y² + 2xy
(4)² = x² + y² + 2(2)
x² + y² = 16 - 4 = 12
Hence, (3) is the correct option.
Question 12
1 / -0

Simplify:

A

B

C

D

Solution

^{₌
Therefore, option 2 is the correct answer.}
Question 13
1 / -0

If x = and y = , find the value of (x – y)(x + y).

A

B

C

D

Solution

(x – y)(x + y) = x²- y²Substituting the values of x and y as given, we get
x²- y²= =
Question 14
1 / -0

Simplify:

A
1

B
10

C
100

D
12

E
15

Solution

=

= 100
Question 15
1 / -0

Find the missing term (blank) in the following equation:

2x²y + 4xz + 6xy = ____ (xy + 2z + 3y)

A
2

B
2y

C
2x

D
2xy

Solution

2x²y + 4xz + 6xy
= 2x(xy + 2z + 3y)
Hence, option 3 is correct.