Class 9 Practice Level 2 – Polynomials - set - 2

Total questions: 25

What is the remainder when $ \displaystyle {3{{x}^{3}}-5{{x}^{2}}+4x-2}$ is divided by $\displaystyle x-1$ ?

Topic: Polynomial Division

-1

None

Find the zeroes of the polynomial $ \displaystyle {2{{x}^{2}}-3x-2}$ .

Topic: Zeroes of Polynomials

$ \displaystyle -2,\frac{1}{2}$

$ \displaystyle \frac{3}{2},-1$

$ \displaystyle 2,-\frac{1}{2}$

$ \displaystyle -\frac{3}{2},1$

None

Use the identity $ \displaystyle {{(a+b)}^{3}}={{a}^{3}}+3{{a}^{2}}b+3a{{b}^{2}}+{{b}^{3}}$ to expand $ \displaystyle {{(x-1)}^{3}}$.

Topic: Polynomial Identities

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

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

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

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

None

Evaluate the polynomial $ \displaystyle 2{{x}^{3}}-{{x}^{2}}+3x-1\text{ at }x=1.$

Topic: Polynomial Evaluation

None

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

Topic: Polynomial Subtraction

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

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

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

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

None

Find the zeroes of the polynomial $ \displaystyle {{x}^{2}}-3x+2.$

Topic: Zeroes of Polynomials

1,2

-1,-2

1,-2

-1,2

None

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

Topic: Multiplication of Polynomials

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

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

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

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

None

What is the quotient when $ \displaystyle 4{{x}^{4}}-2{{x}^{3}}+{{x}^{2}}-3x+5$ is divided by $ \displaystyle x+2$ ?

Topic: Polynomial Division

$ \displaystyle 4{{x}^{3}}-10{{x}^{2}}+21x-45$

$ \displaystyle 4{{x}^{3}}-8{{x}^{2}}+17x-33$

$ \displaystyle 4{{x}^{3}}-10{{x}^{2}}+21x-43$

$ \displaystyle 4{{x}^{3}}-10{{x}^{2}}+21x-39$

None

Find the coefficient of $ \displaystyle {{x}^{3}}$ in the polynomial $ \displaystyle 2{{x}^{4}}-3{{x}^{3}}+{{x}^{2}}-5x+1.$

Topic: Coefficients

-3

None

10.

Use the identity $ \displaystyle {{(a+b)}^{2}}={{a}^{2}}+2ab+{{b}^{2}}\text{ to expand }{{(x+4)}^{2}}.$

Topic: Polynomial Identities

$ \displaystyle {{x}^{2}}+8x+16$

$ \displaystyle {{x}^{2}}+4x+16$

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

$ \displaystyle {{x}^{2}}+4x+8$

None

11.

Evaluate the polynomial $ \displaystyle {{x}^{2}}-2x+1\text{ at }x=-1.$

Topic: Polynomial Evaluation

-2

None

12.

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

Topic: Factorization

(x-3) (x-3)

(x-3) (x+3)

(x+3) (x+3)

(x+9) (x-1)

None

13.

Use the identity $ \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

14.

If $\displaystyle x=1$ is a zero of the polynomial $ \displaystyle {{x}^{3}}-a{{x}^{2}}+bx-c$, find the value of a+b+c.

Topic: Zeroes of Polynomials

None

15.

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

Topic: Polynomial Division

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

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

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

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

None

16.

Using the identity $ \displaystyle {{(a-b)}^{2}}={{a}^{2}}-2ab+{{b}^{2}}\text{ to expand }{{(x-5)}^{2}}$

Topic: Polynomial Identities

$\displaystyle {\text{ }{{x}^{2}}-10x+10}$

$\displaystyle {{{x}^{2}}-5x+25}$

$\displaystyle {{{x}^{2}}-10x+25}$

$\displaystyle {\text{ }{{x}^{2}}-5x+10}$

None

17.

What is the product of the polynomials $\displaystyle \left( {x-1} \right)\text{ and }\left( {{{x}^{2}}+x+1} \right)$ ?

Topic: Multiplication of Polynomials

$ \displaystyle {{x}^{3}}-1$

$ \displaystyle {{x}^{3}}+1$

$ \displaystyle {{x}^{3}}+x+1$

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

None

18.

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

Topic: Polynomial Evaluation

None

19.

What is the quotient when $ \displaystyle 3{{x}^{4}}-2{{x}^{3}}+4{{x}^{2}}-5x+1$ is divided by x-1?

Topic: Polynomial Division

$ \displaystyle 3{{x}^{3}}+{{x}^{2}}+5x-6$

$ \displaystyle 3{{x}^{3}}+{{x}^{2}}+5x-4$

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

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

None

20.

Find the coefficient of $ \displaystyle {{x}^{4}}$ in the polynomial $ \displaystyle 5{{x}^{4}}-3{{x}^{3}}+2{{x}^{2}}-x+1$.

Topic: Coefficients

-3

None

21.

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

Topic: Polynomial Identities

$ \displaystyle 8{{x}^{3}}+36{{x}^{2}}+54x+27$

$ \displaystyle 8{{x}^{3}}+36{{x}^{2}}+54x+9$

$ \displaystyle 8{{x}^{3}}+18{{x}^{2}}+36x+27$

$ \displaystyle 8{{x}^{3}}+18{{x}^{2}}+54x+9$

None

22.

Evaluate the polynomial $\displaystyle {{x}^{3}}-3{{x}^{2}}+2x-1\text{ at }x=2.$

Topic: Polynomial Evaluation

-1

None

23.

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

Topic: Polynomial Subtraction

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

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

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

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

None

24.

Factorize the polynomial $ \displaystyle {{x}^{2}}+5x+6.$

Topic: Factorization

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

$ \displaystyle \left( {x+1} \right)\left( {x+6} \right)$

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

$ \displaystyle \left( {x+3} \right)\left( {x+1} \right)$

None

25.

If $\displaystyle x=2$ is a zero of the polynomial $ \displaystyle {{{x}^{3}}-5{{x}^{2}}+kx-10}$, find the value of k.

Topic: Zeroes of Polynomials

None

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Class 9 Practice Level 2 – Polynomials - set - 2

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