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This mock test of Test: Introduction To Polynomials for Class 9 helps you for every Class 9 entrance exam.
This contains 20 Multiple Choice Questions for Class 9 Test: Introduction To Polynomials (mcq) to study with solutions a complete question bank.
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QUESTION: 1

If x + 2 is a factor of x^{3} – 2ax^{2} + 16, then value of a is

Solution:

QUESTION: 2

A polynomial of degree ‘3’ is called

Solution:

QUESTION: 3

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

Solution:

x²+ 5x - 6 = 0

x² - x + 6x - 6

x (x-1) + 6 (x-1)

(x-1) (x+6)

x = 1; x = -6

QUESTION: 4

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

Solution:

3^3+5^3-8^3=27+125-512

=152-512

=-360

QUESTION: 5

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

Solution:

⇒ x²+ 5x - 6 = 0

⇒ x²+ 6x -x - 6 = 0

⇒ x(x+6) -1(x+6) = 0

⇒ (x-1) (x+6) = 0

⇒ x = 1, -6

QUESTION: 6

If x + 2 is a factor of x^{3} – 2ax^{2} + 16, then value of a is

Solution:

use factor theorem as x+2 is factor of

x³-2ax²+16 so put x = -2 and equate the equation to 0

so putting x = -2

(-2)³-2a(-2)²+16 =0

-8-8a+16=0

-8a = -8

a = 8/8= 1

So,

a = 1

QUESTION: 7

Which of the following is not a quadratic polynomial?

Solution:

QUESTION: 8

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

Solution:

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

QUESTION: 9

Zero of the polynomial p(x) where p (x) = ax, a ≠ 0 is:

Solution:

QUESTION: 10

If x + 2 is a factor of x^{3} – 2ax^{2} + 16, then value of a is

Solution:

QUESTION: 11

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

Solution:

p(-2) = 7 - 3(-2) + 2(-2)^{2}

= 7+6+8 = 21

QUESTION: 12

A linear polynomials has how many zeros

Solution:

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.

QUESTION: 13

If one of the factor of x^{2} + x – 20 is (x + 5). Find the other

Solution:

QUESTION: 14

Which of the following is a quadratic polynomial in one variable?

Solution:

QUESTION: 15

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

Solution:

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.

QUESTION: 16

Find the value of the polynomial 6 – 4x + 3x^{2} at x = 3

Solution:

QUESTION: 17

Degree of zero polynomial is:

Solution:

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.

QUESTION: 18

Zero of a zero polynomial is:

Solution:

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.

QUESTION: 19

What is the coefficient of x in x^{3} + 3x^{2} - 2x - 1

Solution:

QUESTION: 20

The degree of the polynomial x^{4} – 3x^{3} + 2x^{2} – 5x + 3 is:

Solution:

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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