CLASS IX POLYNOMIAL TEST

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| By Hitanshu Kapoor

Hitanshu Kapoor

Community Contributor

Quizzes Created: 1 | Total Attempts: 1,670

Questions: 6 | Attempts: 1,670 | Updated: Jan 15, 2024

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Questions and Answers

1.

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)
Correct Answer
A. 3x + 1) (2x + 3)

Explanation
The given expression is a quadratic trinomial. To factorize it, we can look for two binomials that multiply together to give the trinomial. In this case, the factors are (3x + 1) and (2x + 3). When we expand these binomials using the distributive property, we get 6x^2 + 11x + 3, which matches the original expression. Therefore, the correct factorization is 3x + 1) (2x + 3).

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5
1
2.

√12 X √15 is equal to:
- A.
  
  5√6
- B.
  
  6√5
- C.
  
  10√5
- D.
  
  √25
Correct Answer
B. 6√5

Explanation
When multiplying square roots, you can simply multiply the numbers inside the square roots and keep the square root symbol. In this case, √12 multiplied by √15 equals √180. Simplifying further, you can break down 180 into its prime factors: 2 x 2 x 3 x 3 x 5. Taking out pairs of the same number, we are left with 2 x 3 x √5, which can be simplified to 6√5. Therefore, the correct answer is 6√5.

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14
0
3.

The value of the polynomial 7x⁴ + 3x² - 4, when x = - 2 is:
- A.
  
  100
- B.
  
  110
- C.
  
  120
- D.
  
  130
Correct Answer
C. 120

Explanation
When we substitute x = -2 into the given polynomial, we get 7(-2)^4 + 3(-2)^2 - 4. Simplifying this expression, we have 7(16) + 3(4) - 4, which equals 112 + 12 - 4 = 120. Therefore, the value of the polynomial when x = -2 is 120.

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7
0
4.

What is the degree of a zero polynomial?
- A.
  
  0
- B.
  
  1
- C.
  
  Any natural number
- D.
  
  Not defined
Correct Answer
D. Not defined

Explanation
The degree of a polynomial is defined as the highest power of the variable in the polynomial. However, a zero polynomial is a polynomial in which all the coefficients are zero. Since there are no terms with non-zero coefficients in a zero polynomial, it does not have a highest power or degree. Therefore, the degree of a zero polynomial is not defined.

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4
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5.

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
Correct Answer
C. 2

Explanation
If x + 1 is a factor of the polynomial 2x^2 + kx, it means that when x = -1, the polynomial will equal to zero. Substituting -1 into the polynomial, we get 2(-1)^2 + k(-1) = 0. Simplifying this equation, we get 2 - k = 0, which means k = 2. Therefore, the value of k is 2.

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9
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6.

If p + q+ r = 0, then p³ + q³ + r³ is equal to
- A.
  
  0
- B.
  
  3abc
- C.
  
  2abc
- D.
  
  Abc
Correct Answer
B. 3abc

Explanation
When p + q + r = 0, it means that the sum of p, q, and r is equal to zero. This can be rearranged as p = -q - r. When we substitute this value of p into the expression p^3 + q^3 + r^3, we get (-q - r)^3 + q^3 + r^3. Simplifying this expression, we get -3q^2r - 3qr^2. Factoring out a -3qr from this expression, we get -3qr(q + r). Since q + r is equal to -p, we can further simplify the expression to -3qr(-p). This is equal to 3pqr, which can be written as 3abc. Therefore, the correct answer is 3abc.

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5
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Current Version
Jan 15, 2024

Quiz Edited by
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Apr 22, 2020

Quiz Created by
Hitanshu Kapoor

Class Ix Polynomial Test

The factorization of 6x2 + 11x + 3 is:

√12 X √15 is equal to:

The value of the polynomial 7x4 + 3x2 - 4, when x = - 2 is:

What is the degree of a zero polynomial?

If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is:

If p + q+ r = 0, then p3 + q3 + r3 is equal to

The factorization of 6x² + 11x + 3 is:

The value of the polynomial 7x⁴ + 3x² - 4, when x = - 2 is:

If x + 1 is a factor of the polynomial 2x² + kx, then the value of k is:

If p + q+ r = 0, then p³ + q³ + r³ is equal to