Polynomials Test

Result

Polynomials Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

What is the sum of 2xy + 6x + 4y² + 6 and 8 + 4x + 2y² - 4xy?

A
- 10xy + 10x + 6y² + 2

B
6xy + 10x + 6y² + 14

C
- 2xy + 10x + 6y² + 14

D
2xy + 10x + 6y² + 14

Solution
Question 2
1 / -0

What is the product of and ?

A
12x²y + 32xy² + + xy

B
12xy + 32xy² + + 3x²y

C
xy + 10x²y + (8/5)y² + 3xy

D
12xy² + 32x²y + y² + xy

Solution

=
=
= 12x²y + 32xy² + y² + xy
Question 3
1 / -0

What is the value of (2x + 3y)²– (2x)²?

A
3y(4x + 3y)

B
y(4x + 3y)

C
2y(4x + 2y)

D
3y(3x + 4y)

Solution

(2x + 3y)² – (2x)²
We know that a² – b² = (a + b) (a – b).
(2x + 3y)² – (2x)² = (2x + 3y + 2x)(2x + 3y – 2x)
= (4x + 3y)(3y)
Question 4
1 / -0

If (104)² = 10000 + A² + 200A, then what is the value of A?

A
4

B
2

C
1

D
3

Solution

(104)² = (100 + 4)²
Using (a + b)² = a² + b²+ 2ab, we get
(100 + 4)² = 10000 + 4² + 200(4)
A = 4
Question 5
1 / -0

What is the result of [(2x - 6)(2x - 5) + (x + 6)(x - 5)]?

A
18x + 60

B
5x² - 21x

C
5x² + 21x + 60

D
5x² + 21

Solution

We know,
(x + a)(x + b) = x² + (a + b)x + ab
(2x - 6)(2x - 5) = (2x)² + (-6 - 5)2x + (-6)(-5)
= 4x² - 22x + 30 ... (i)
(x + 6)(x - 5) = x² + (6 -5)x + (6)(-5)
= x² + x - 30 ... (ii)
Now, on adding (i) and (ii), we get
x² + x - 30 + 4x² - 22x + 30
= 5x² - 21x
Hence, (2) is the correct option.
Question 6
1 / -0

What will you get on multiplying (2z + 3x + 2) by (-2x + 2 - 3z)?

A
-6x² - 6z² - 13xz + 2x - 2z + 4

B
6x² - 6z² - 13xz + 10x - 2z + 4

C
6x² - 6z² + 10x + 4

D
-6x² - 6z² - 13xz + 2x - 2z - 4

Solution

(2z + 3x + 2) (-2x + 2 - 3z)
2z (-2x + 2 - 3z) + 3x (-2x + 2 - 3z) + 2 (-2x + 2 - 3z)
= -4xz + 4z - 6z² - 6x² + 6x - 9xz - 4x + 4 - 6z
= -6x² - 6z² - 13xz + 2x - 2z + 4
Question 7
1 / -0

What is the sum of 2ab + 2 – 4a²b² – 2a, – 4ab + 4a² – 3b and 2 + 3a – 4b + 6a² + 2a²b²?

A
2a²b² + 10a² + 10a² + a – 7 + 4

B
2a²b² – 2ab + 10a² + a – 7b + 4

C
– 2a²b² – 2ab + 10a² – 7a + 4

D
– 2a²b² – 2ab + 10a² + a – 7b + 4

Solution
Question 8
1 / -0

If 301 302 = 90000 + (m + n) 300 + mn, what is the value of (m n)?

A
2

B
1

C
3

D
0

Solution

301 302 = (300 + 1)(300 + 2)
Use identity (x + a)(x + b) = x² + (a + b)x + ab.
Putting x = 300, a = 1 and b = 2 in the above equation, we get
90000 + (1 + 2)300 + 1 2
Now comparing it with the original equation given in the question, we get
m n = 2
Hence, (1) is the correct option.
Question 9
1 / -0

What is the value of z(x – y) for x = 4, y = 1 and z = 2?

A
6

B
5

C
2

D
1

Solution

z(x - y) = a
x = 4, y = 1, z = 2
a = 2(4 - 1) = 2(3) = 6
Hence, (1) is the correct option.
Question 10
1 / -0

Find the simplified form of (x² – 3)(x + 3) + 9.

A
– x(x² + 3x + 3)

B
– x(x² + 3x – 3)

C
x(x² + 3x – 3)

D
x(x² + 3x + 3)

Solution

(x² – 3) (x + 3) + 9
= x³ + 3x² – 3x – 9 + 9
= x³ + 3x² – 3x
= x(x² + 3x – 3)
Question 11
1 / -0

If 2a + b = 45 and b = 3, find the value of a.

A
16

B
20

C
21

D
25

Solution

2a + b = 45, b = 3
2a + 3 = 45
2a = 45 - 3
2a = 42
a = = 21
Question 12
1 / -0

If 3x – 7y = 10 and xy = –2, what is the value of 9x² + 49y²?

A
16

B
142

C
104

D
18

Solution

3x – 7y = 10
Squaring both sides
9x² + 49y² - 42xy = 100
9x² + 49y² + 84 = 100 ( Given xy = -2)
9x² + 49y² = 16
Question 13
1 / -0

If x + = 5, find the value of x² + .

A
5

B
25

C
10

D
23

Solution

x + = 5

Squaring both sides,
= (5)²

x² + + 2 = 25

x² + = 25 - 2 = 23
Question 14
1 / -0

Simplify: (7x + 8y)² + (7x - 8y)²

A
49x²

B
98x²

C
98x² + 128y²

D
49x² + 64y²

Solution

(7x + 8y)² + (7x - 8y)²
= (7x)² + (8y)² + 2(7x)(8y) + (7x)² + 8y² - 2(7x)(8y)
= 49x² + 64y² + 49x² + 64y²
= 98x² + 128y²
Question 15
1 / -0

Simplify the following expression:

A
x + 7

B
x - 7

C
x - 2

D
x + 2

Solution

= x + 2