Class 9 Practice Level 2 - Polynomials - Set 1

Total questions: 25

$ \displaystyle \text{factorize of polynomials }{{x}^{2}}-5x+6.$

Topic: Factorization of polynomials

$ \displaystyle \left( {x-2} \right)\left( {x-3} \right)$

$ \displaystyle \left( {x+2} \right)\left( {x-3} \right)$

$ \displaystyle \left( {x-2} \right)\left( {x+3} \right)$

$ \displaystyle \left( {x+2} \right)\left( {x+3} \right)$

None

$ \displaystyle \text{Find the roots of the polynomial }{{x}^{2}}+7x+10.$

Topic: Roots of Polynomials

$ \displaystyle -2,-5$

$ \displaystyle 2,-5$

$ \displaystyle -2,5$

$ \displaystyle 2,5$

None

$ \displaystyle \text{Divide 2}{{x}^{3}}+3{{x}^{2}}-x-2\ \text{by }x+1.$

Topic: Division of polynomials

$ \displaystyle \text{2}{{x}^{2}}+x-2$

$ \displaystyle \text{2}{{x}^{2}}+x-1$

$ \displaystyle \text{2}{{x}^{2}}+x+1$

$ \displaystyle \text{2}{{x}^{2}}+3x-2,$

None

FInd the remainder of the polynomial $ \displaystyle \text{3}{{x}^{3}}+2{{x}^{2}}-4x+5$ is divided by $ \displaystyle x-1.$

Topic: Remainder theorem

None

use the identity $ \displaystyle {{\left( {a+b} \right)}^{2}}={{a}^{2}}+2ab+{{b}^{2}}$ to expand $ \displaystyle {{\left( {2x+3} \right)}^{2}}$

Topic: Polynomial Identities

$ \displaystyle 4{{x}^{2}}+12x+9$

$ \displaystyle 4{{x}^{2}}+6x+9$

$ \displaystyle 4{{x}^{2}}+12x+6$

$ \displaystyle 4{{x}^{2}}+6x+6$

None

If one is zero of polynomial $=\displaystyle {{x}^{2}}-4x+4$ is 2,what is the other zero ?

Topic: Zeroes of Polynomials

-2

None

verify the identity $ \displaystyle {{a}^{3}}+{{b}^{3}}=\left( {a+b} \right)\left( {{{a}^{2}}-ab+{{b}^{2}}} \right)$ for a=2 and b=3.

Topic: Polynomial Identities

35=35

36=36

37=37

38=38

None

Find the coefficient of $ \displaystyle x$ in the polynomial $ \displaystyle 4{{x}^{3}}+3{{x}^{2}}+2x-7.$

Topic: Coefficients

-3

-7

None

what is the degree of the polynomial $\displaystyle 3{{x}^{4}}+5{{x}^{3}}+{{x}^{2}}-7$ ?

Topic: Degree of Polynomials

None

10.

which of the following is not a polynomials?

Topic: Identifying Polynomials

$ \displaystyle 3{{x}^{2}}+2x-5$

$ \displaystyle 4{{x}^{3}}-x+7$

$ \displaystyle {{x}^{2}}+\frac{1}{x}$

$ \displaystyle {{x}^{4}}-3{{x}^{2}}+2x-1$

None

11.

If $ \displaystyle x=1$ is a zero of the polynomial $ \displaystyle 2{{x}^{3}}-3{{x}^{2}}+kx-1$ , find the value of k:

Topic: Zero Polynomial

-2

None

12.

Using the remainder theorem ,find the remainder when $ \displaystyle {{x}^{3}}-3{{x}^{2}}+4x-2$ is divided by $\displaystyle x-2$ .

Topic: Remainder theorem

-2

None

13.

Factorize the polynomial $ \displaystyle {{x}^{2}}+6x+9$ .

Topic: Factorization

$ \displaystyle {{\left( {x+3} \right)}^{2}}$

$ \displaystyle {{\left( {x-3} \right)}^{2}}$

$ \displaystyle \left( {x+3} \right)\left( {x-3} \right)$

$ \displaystyle \left( {x+6} \right)\left( {x+3} \right)$

None

14.

What is the quotient when $ \displaystyle 4{{x}^{3}}+2{{x}^{2}}-x+1$ is divided by $ \displaystyle x+1$ .

Topic: Polynomial Division

$ \displaystyle 4{{x}^{2}}-2x+1$

$ \displaystyle 4{{x}^{2}}+2x-1$

$ \displaystyle 4{{x}^{2}}-x+1$

$\displaystyle 4{{x}^{2}}+x-1$

None

15.

Using the identify $\displaystyle {{\left( {a-b} \right)}^{2}}={{a}^{2}}-2ab+{{b}^{2}}$ to expand $ \displaystyle {{\left( {3x-4} \right)}^{2}}$ .

Topic: Polynomial Identities

$ \displaystyle 9{{x}^{2}}-24x+16$

$ \displaystyle 9{{x}^{2}}-12x+16$

$ \displaystyle 9{{x}^{2}}+24x+16$

$ \displaystyle 9{{x}^{2}}-24x-16$

None

16.

Evaluate the polynomial $ \displaystyle {{x}^{2}}-4x+3\text{ at }x=2$

Topic: Polynomial Evaluation

-1

None

17.

Subtract $ \displaystyle 3{{x}^{2}}-4x+5$ from $ \displaystyle 5{{x}^{2}}-2x+1$ .

Topic: Polynomial Subtraction

$ \displaystyle 2{{x}^{2}}+2x-4$

$ \displaystyle 2{{x}^{2}}-2x-4$

$ \displaystyle 2{{x}^{2}}+2x+4$

$ \displaystyle 2{{x}^{2}}-2x+4$

None

18.

Find the zeroes of the polynomial $ \displaystyle {{x}^{2}}-x-6.$

Topic: Zeroes of Polynomials

2,-3

-2,3

-2,-3

2,3

None

19.

what is the product of the polynomials $ \displaystyle {x+2}$ and $ \displaystyle {{{x}^{2}}-2x+3}$

Topic: Multiplication of Polynomials

$\displaystyle {{x}^{3}}+x+6$

$\displaystyle {{x}^{3}}-x+6$

$ \displaystyle {{x}^{3}}+2{{x}^{2}}+4x+6$

$ \displaystyle {{x}^{3}}+2{{x}^{2}}+x+6$

None

20.

Using the reaminder theorem,find the remainder when $ \displaystyle 2{{x}^{3}}-{{x}^{2}}+3x-5$ is divided by $ \displaystyle x-1$ .

Topic: Remainder theorem

-1

-2

None

21.

Use the identify $\displaystyle {{\left( {a+b} \right)}^{3}}={{a}^{3}}+3{{a}^{2}}b+3a{{b}^{2}}+{{b}^{3}}$ to expand $ \displaystyle {{\left( {x+2} \right)}^{3}}$ .

Topic: Polynomial Identities

$ \displaystyle {{x}^{3}}+6{{x}^{2}}+12x+8$

$ \displaystyle {{x}^{3}}+3{{x}^{2}}+6x+8$

$\displaystyle {{x}^{3}}+6{{x}^{2}}+6x+8$

$ \displaystyle {{x}^{3}}+3{{x}^{2}}+6x+6$

None

22.

Evalute the polynomial $ \displaystyle 3{{x}^{2}}-5x+2$ at $ \displaystyle x=-1$

Topic: Polynomial Evaluation

-10

-2

None

23.

Find the coefficient of $ \displaystyle {{{x}^{2}}}$ in the polynomial $ \displaystyle 7{{x}^{3}}-4{{x}^{2}}+5x-6$ ..

Topic: Coefficients

-4

-6

None

24.

What is the product of the polynomials $ \displaystyle 2x-3$ and $ \displaystyle {{x}^{2}}+x+1$ .

Topic: Multiplication of Polynomials

$ \displaystyle 2{{x}^{3}}-3{{x}^{2}}+2x+3$

$ \displaystyle 2{{x}^{3}}-{{x}^{2}}-x-3$

$ \displaystyle 2{{x}^{3}}-3{{x}^{2}}-x-3$

$ \displaystyle 2{{x}^{3}}-3{{x}^{2}}-2x-3$

None

25.

Use the identify $\displaystyle {{a}^{3}}-{{b}^{3}}=\left( {a-b} \right)\left( {{{a}^{2}}+ab+{{b}^{2}}} \right)$ to factorize $ \displaystyle {{x}^{3}}-8$ .

Topic: Polynomial Identities

$ \displaystyle \left( {x-2} \right)\left( {{{x}^{2}}+2x+4} \right)$

$ \displaystyle \left( {x+2} \right)\left( {{{x}^{2}}+2x+4} \right)$

$ \displaystyle \left( {x-2} \right)\left( {{{x}^{2}}-2x+4} \right)$

$ \displaystyle \left( {x+2} \right)\left( {{{x}^{2}}-2x+4} \right)$

None

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Class 9 Practice Level 2 - Polynomials - Set 1

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