Algebraic Expressions est

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Algebraic Expressions est - 1

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Weekly Quiz Competition

Question 1
1 / -0

The information in which alternative is incorrectly matched?

A

Polynomial Type

x² + y² Binomial

B

Polynomial Type

x + y Binomial

C

Polynomial Type

x³ Trinomial

D

Polynomial Type

xyz Monomial

Solution

An expression that contains one term is called a monomial, that which contains two terms is called a binomial, and that which contains three terms is called a trinomial.

It can be seen that the expression x³ has only one term. Therefore, it is a monomial.
Question 2
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Which equation correctly represents the statement, ‘Twice the sum of x and 3 is less than 24 by 8’?

A
2(x + 3) − 8 = 24

B
28 − 2x + 3 = 24

C
24 − 2(x + 3) = 8

D
24 − (2x + 3) = 8

Solution

Sum of x and 3 = x + 3

∴ Twice the sum of x and 3 = 2 (x + 3)

According to the given information:

24 − 2 (x + 3) = 8

Thus, the required equation is 24 − 2 (x + 3) = 8
Question 3
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The information in which alternative is correctly matched?

A

Polynomial Coefficient of x² Coefficient of x

7x² + 2x + 3 7 2

B

Polynomial Coefficient of x² Coefficient of x

2x² + 3yz + x 2 0

C

Polynomial Coefficient of x² Coefficient of x

9y² + 6x² + 2yz + 3x 9 3

D

Polynomial Coefficient of x² Coefficient of x

4x² + 2y² + 4z² − 2x 4 2

Solution

The numerical factor of a term is said to be its coefficient.

In the expression 7x² + 2x + 3, the coefficient of x² is 7 and the coefficient of x is 2.
Question 4
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Use the following information to answer the next question.

In a race, each runner is required to complete two rounds of the track. The time taken by Manish to cover the second round was 10 seconds less than twice the time taken by him to cover the first round. In total, he took 71 seconds to complete the race.

If Manish took x seconds to cover the first round, then which equation represents the given situation?

A
10 – 2x = 71

B
3x – 10 = 71

C
10 – 3x = 71

D
2x – 10 = 71

Solution

Time taken to cover the first round = x seconds

It is given that the time taken by him to cover the second round was 10 seconds less than twice the time taken to cover the first round.

Therefore, time taken to cover the second round = (2x – 10) s

It is also given that total time taken to complete the race = 71 s

∴x + 2x – 10 = 71

∴3x – 10 = 71

Thus, the equation 3x – 10 = 71 represents the given situation.

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Polynomial	Coefficient of x²	Coefficient of x
2x² + 3yz + x	2	0

Polynomial	Type
x² + y²	Binomial

Polynomial	Type
x + y	Binomial

Polynomial	Type
x³	Trinomial

Polynomial	Type
xyz	Monomial

Algebraic Expressions est - 1

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Algebraic Expressions est - 1

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Question 1

Polynomial Type x2 + y2 Binomial

Polynomial Type x + y Binomial

Polynomial Type x3 Trinomial

Polynomial Type xyz Monomial

Solution

Question 2

2(x + 3) − 8 = 24

28 − 2x + 3 = 24

24 − 2(x + 3) = 8

24 − (2x + 3) = 8

Solution

Question 3

Polynomial Coefficient of x2 Coefficient of x 7x2 + 2x + 3 7 2

Polynomial Coefficient of x2 Coefficient of x 2x2 + 3yz + x 2 0

Polynomial Coefficient of x2 Coefficient of x 9y2 + 6x2 + 2yz + 3x 9 3

Polynomial Coefficient of x2 Coefficient of x 4x2 + 2y2 + 4z2 − 2x 4 2

Solution

Question 4

10 – 2x = 71

3x – 10 = 71

10 – 3x = 71

2x – 10 = 71

Solution

Time taken to cover the first round = x seconds

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Polynomial Type

x² + y² Binomial

Polynomial Type

x + y Binomial

Polynomial Type

x³ Trinomial

Polynomial Type

xyz Monomial

Polynomial Coefficient of x² Coefficient of x

7x² + 2x + 3 7 2

Polynomial Coefficient of x² Coefficient of x

2x² + 3yz + x 2 0

Polynomial Coefficient of x² Coefficient of x

9y² + 6x² + 2yz + 3x 9 3

Polynomial Coefficient of x² Coefficient of x

4x² + 2y² + 4z² − 2x 4 2