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Test: Introduction To Polynomials - Grade 9 MCQ


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15 Questions MCQ Test - Test: Introduction To Polynomials

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Test: Introduction To Polynomials - Question 1

If x + 2 is a factor of x3 – 2ax2 + 16, then value of a is

Detailed Solution for Test: Introduction To Polynomials - Question 1

Test: Introduction To Polynomials - Question 2

A polynomial of degree ‘3’ is called

Detailed Solution for Test: Introduction To Polynomials - Question 2
The polynomial ax3 + bx2 + cx + d (where a ≠ 0) is called a cubic polynomial because the highest power of x is 3. The term 'cubic' refers to polynomials of degree three, similar to how 'quadratic' denotes second-degree polynomials. This terminology is standard in algebra when describing polynomial degrees.
Test: Introduction To Polynomials - Question 3

What is the solution to the quadratic equation x² + 7x + 12 = 0?

Detailed Solution for Test: Introduction To Polynomials - Question 3

To solve the quadratic equation x² + 7x + 12 = 0, we use the factorization method.

  • We need to find two numbers that multiply to give 12 (the constant term) and add up to give 7 (the coefficient of x). The numbers 3 and 4 satisfy this because 3 * 4 = 12 and 3 + 4 = 7.

  • Therefore, we can factor the quadratic equation as: (x + 3)(x + 4) = 0

  • Setting each factor equal to zero: x + 3 = 0 → x = -3

  • x + 4 = 0 → x = -4

Test: Introduction To Polynomials - Question 4

If 3 + 5 – 8 = 0, then the value of (3)3 + (5)3 – (8)3 is

Detailed Solution for Test: Introduction To Polynomials - Question 4

To calculate the expression involving cubes, let's break it down step by step:

  • 3 cubed: 33 = 27
  • 5 cubed: 53 = 125
  • 8 cubed: 83 = 512

Now, we can substitute these values into the expression:

33 + 53 - 83 = 27 + 125 - 512

Calculating this step-by-step:

  • First, add 27 and 125: 27 + 125 = 152
  • Then, subtract 512: 152 - 512 = -360

Therefore, the final result is: -360.

Test: Introduction To Polynomials - Question 5

Solution of a quadratic equation x²+ 5x - 6 = 0

Detailed Solution for Test: Introduction To Polynomials - Question 5

⇒ x²+ 5x - 6 = 0

⇒ x²+ 6x -x - 6 = 0

⇒ x(x+6) -1(x+6) = 0

⇒ (x-1) (x+6) = 0

⇒ x = 1, -6

 

Test: Introduction To Polynomials - Question 6

Which of the following is not a quadratic polynomial?​

Detailed Solution for Test: Introduction To Polynomials - Question 6

Therefore, the option that is not a quadratic polynomial is: x – x3

Test: Introduction To Polynomials - Question 7

P of x = ax, a is not equal to 0. find zeros of polynmial

Detailed Solution for Test: Introduction To Polynomials - Question 7

p(x) = ax
p(x) = 0
ax = 0
x = 0/a
x = 0
{0 by something is equals to 0}
Therefore,0 is the zero of the polynomial. 
Checking:-
p(0) = a(0)
= 0

Test: Introduction To Polynomials - Question 8

If p(x) = 7 – 3x + 2x2 then value of p(-2) is:

Detailed Solution for Test: Introduction To Polynomials - Question 8

- To find p(-2), substitute -2 into the function p(x) = 7 - 3x + 2x^2.
- Calculate step-by-step:
- p(-2) = 7 - 3(-2) + 2(-2)2
- This simplifies to 7 + 6 + 2(4)
- Which further simplifies to 7 + 6 + 8
- Adding these together gives: 21.
- Therefore, the value of p(-2) is 21, making option 3 the correct answer.

Test: Introduction To Polynomials - Question 9

A linear polynomials has how many zeros

Detailed Solution for Test: Introduction To Polynomials - Question 9

A linear polynomial has 1 zero.

A quadratic polynomial has 2 zeroes.

A cubic polynomial has 3 zeroes.

In general, any polynomial has as many zeroes as its degree.

Test: Introduction To Polynomials - Question 10

If one of the factor of x2 + x – 20 is (x + 5). Find the other

Detailed Solution for Test: Introduction To Polynomials - Question 10

Test: Introduction To Polynomials - Question 11

A cubic polynomial is a polynomial of degree …………

Detailed Solution for Test: Introduction To Polynomials - Question 11

A cubic polynomial is a polynomial of degree 3. A univariate cubic polynomial has the form An equation involving a cubic polynomial is called a cubic equation. A closed-form solution known as the cubic formula exists for the solutions of an arbitrary cubic equation.

Test: Introduction To Polynomials - Question 12

Find the value of the polynomial 6 – 4x + 3x2 at x = 3

Detailed Solution for Test: Introduction To Polynomials - Question 12

To find the value of the polynomial ( 6 - 4x + 3x2 ) at ( x = 3 ):

- Substitute ( x = 3 ) into the polynomial:
=[6 - 4(3) + 3(32)]
- Calculate step-by-step:
=[6 - 4(3) + 3(9)]
=[6 - 12 + 27]
=[21]

Thus, the value of the polynomial at ( x = 3 ) is 21.

Therefore, the correct answer is:
- B: 21

Test: Introduction To Polynomials - Question 13

Degree of zero polynomial is:

Detailed Solution for Test: Introduction To Polynomials - Question 13

A zero polynomial is a polynomial in which all the coefficients are 0.

Let the polynomials highest power variable be x^n as per the above statement x^n = 0 

Now, The degree of the zero polynomial is log0 which is undefined. 

Hence. The degree of zero polynomial is undefined.

Test: Introduction To Polynomials - Question 14

Zero of a zero polynomial is:

Detailed Solution for Test: Introduction To Polynomials - Question 14

Zero of the zero polynomial is any real number.
e.g., Let us consider zero polynomial be 0(x-k), where k is a real number For determining the zero, put x-k = 0 ⇒ x = k Hence, zero of the zero polynomial be any real number. 

Test: Introduction To Polynomials - Question 15

The degree of the polynomial x4 – 3x3 + 2x2 – 5x + 3 is:

Detailed Solution for Test: Introduction To Polynomials - Question 15

The degree refers to the highest power of the polynomial. In this polynomial X has highest power 4.So the degree of polynomial is 4.

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