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This mock test of Test: Polynomials - 2 for Class 9 helps you for every Class 9 entrance exam.
This contains 25 Multiple Choice Questions for Class 9 Test: Polynomials - 2 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

√2 is a polynomial of degree

Solution:

QUESTION: 2

If a+b+c = 0, then a^{3}+b^{3}+c^{3 }is equal to

Solution:

QUESTION: 3

A polynomial containing two nonzero terms is called a ________.

Solution:
**Examples of binomials.**

A binomial is a mathematical expression with two terms.

binomial

All of these examples are binomials. Study them for a bit, and see if you can spot a pattern. The following is a list of what binomials must have:

They must have two terms.

If the variables are the same, then the exponents must be different.

Exponents must be whole positive integers. They cannot be negatives or fractions.

A term is a combination of numbers and variables. In the example 3x + 5, our first term is 3x, and our second term is 5. Terms are separated by either addition or subtraction. In our first example, notice how the 3x and 5 are separated by addition. In the last example, we have a binomial whose two terms both have the same variable s. Notice how each term has its variable to a different exponent. The first term has an exponent of 5, and the second term has an exponent of 4. While we can have fractions for our numbers, we cannot have fractional exponents.

Here are some examples of expressions that are not binomials.

QUESTION: 4

The expanded form of (3x−5)^{3} is

Solution:

Let a = 3x and b = 5 (3x)³ - (5)³ - 3×3x×5(3x- 5) = 27x³ - 125 -45x ( 3x -5) = 27x³ -125 - 135x² + 225x = 27x³ - 135x² + 225x - 125

QUESTION: 5

Solution:

X+ 1/x = 7 then, cubing both side = (x +1/x)³ = (7)³ = x³ + 1/x³ + 3×X×1/X (x+1/x) = 343 = x³ +1/x³ +3(7) = 343 =x³ +1/x³ +21 =343 = x³ +1/x³ =343 - 21 = x³ +1/x³ = 322

QUESTION: 6

Degree of the polynomial 4x^{4} + 0x^{3} + 0x^{5} + 5x + 7 is:

Solution:
Degree is the highest exponent of any value in an equation. Here, this highest exponent is 4. Therefore, 4 is the degree of the given equation.

QUESTION: 7

(x + 1) is a factor of the polynomial

Solution:

QUESTION: 8

A polynomial containing three nonzero terms is called a ________.

Solution:

QUESTION: 9

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

Solution:

QUESTION: 10

Solution:

QUESTION: 11

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

Solution:

QUESTION: 12

If 10x−4x^{2}−3, then the value of p(0)+p(1) is

Solution:

QUESTION: 13

The coefficient of x^{3} in 2x+x^{2}−5x^{3}+x^{4} is

Solution:

QUESTION: 14

If both x - 2 and are the factors of px^{2} + 5x + r, then

Solution:

Let f(x) = px^{2} + 5 x + r

If (x - 2) is a factor of f (x), then by factor theorem

f(2) = 0 | x - 2 = 0 ⇒ x = 2

⇒ p(2)^{2} + 5(2) + r = 0

⇒ 4p + r + 10 = 0 ...(1)

If is a factor of f (x), then by factor theorem,

Subtracting (2) from (1), we get

3p - 3r = 0

⇒ p = r

QUESTION: 15

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

Solution:

QUESTION: 16

The value of the polynomial 5x−4x^{2}+35, when x = −1 is

Solution:

QUESTION: 17

If x^{2}+kx+6 = (x+2)(x+3), then the value of ‘k’ is

Solution:

QUESTION: 18

The remainder when the polynomial x^{4}+2x^{3}−3x^{2}+x−1 is divided by (x−2) is

Solution:

QUESTION: 19

The remainder obtained when the polynomial p(x) is divided by (b – ax) is

Solution:

QUESTION: 20

The value of x^{3}+y^{3}+15xy−125 when x+y = 5 is

Solution:

X³+y³+15xy-125

=x³ + y³ +3 xy ×5 - 125

=x³ + y³ +3xy(x+y) - (5)³

= (x+y) ³ - (5)³

=(5)³ - (5)³

=0

QUESTION: 21

If p(x) = x + 3, then p(x) + p(-x) is equal to

Solution:

Given p(x) = x+3, put x = -x in the given equation, we get p(-x) = -x+3

Now, p(x)+ p(-x) = x+ 3+ (-x)+ 3=6

QUESTION: 22

One of the factors of (16y^{2}−1)+(1−4y)^{2} is

Solution:

QUESTION: 23

If the polynomial x^{3}−6x^{2}+ax+3 leaves a remainder 7 when divided by (x−1), then the value of ‘a’ is

Solution:

QUESTION: 24

Solution:

QUESTION: 25

The value of (a^{2}−b^{2})^{3}+(b^{2}−c^{2})3+(c^{2}−a^{2})^{3} is

Solution:
Let (aÂ²-bÂ²) =x , (bÂ²-cÂ²) =y , (cÂ²-aÂ²) = z we know that a+b+ c=0 and, aÂ³ + bÂ³ + cÂ³ = 3abc so, 3(a+b)(a-b)(b+c) (b-c)(c+a)(c-a) = 3(a+b)(b+c)(c+a)(a-b)(b-c)(c-a)

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