Class 9 Practice Level 3 – Polynomials – set – 2

Total questions: 15

Divide $ \displaystyle {{x}^{4}}-4{{x}^{3}}+6{{x}^{2}}-4x+1\ \text{by }x-1$ and find the quotient and remainder.

Topic: Polynomial Division

$ \displaystyle {{x}^{3}}-3{{x}^{2}}+3$ remainder 0

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

$ \displaystyle {{x}^{3}}-3{{x}^{2}}+1$ remainder 0

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

None

Find all the roots of the polynomial $ \displaystyle {{x}^{3}}-6{{x}^{2}}+11x-6.$

Topic: Finding Roots

1, 2, 3

0, 2, 3

1, 2, –3

1, –2, 3

None

Using the factor theorem, determine if $ \displaystyle {x-3}$ is a factor of $ \displaystyle {{x}^{4}}-81$.

Topic: Factor Theorem

Yes

Cannot determine

Both

None

Factor $ \displaystyle {{x}^{4}}-5{{x}^{2}}+4$ completely.

Topic: Polynomial Factorization

$ \displaystyle \left( {{{x}^{2}}-1} \right)\left( {{{x}^{2}}-4} \right)$

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

$ \displaystyle \left( {x-1} \right)\left( {x+1} \right)\left( {x-2} \right)\left( {x+2} \right)$

$ \displaystyle \left( {{{x}^{2}}-4} \right)\left( {{{x}^{2}}+1} \right)$

None

Evaluate the polynomial $ \displaystyle p\left( x \right)=2{{x}^{3}}-3{{x}^{2}}+x-5\text{ at }x=-1.$

Topic: Evaluation of Polynomials

–11

–7

None

Divide $ \displaystyle 3{{x}^{3}}+5{{x}^{2}}-2x+4\text{ by }x+2$ and find the remainder.

Topic: Long Division of Polynomials

None

Solve for $ \displaystyle x$ in the equation $ \displaystyle {{{x}^{3}}+3{{x}^{2}}+3x+1=0.}$

Topic: Polynomial Equations

$ \displaystyle x=-1$

$ \displaystyle x=-3$

$ \displaystyle x=0$

$ \displaystyle x=1$

None

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

Topic: Evaluating Remainders

109

120

107

None

Which of the following identities is true?

Topic: Polynomial Identities

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

$ \displaystyle {{x}^{2}}+2xy+{{y}^{2}}={{\left( {x+y} \right)}^{2}}$

Both

Neither

None

10.

What is the value of $ \displaystyle p\left( {-2} \right)$ for the polynomial $ \displaystyle p\left( x \right)={{x}^{3}}+4{{x}^{2}}+4x+1$?

Topic: Finding the Value

–1

–2

None

11.

Find the derivative of $ \displaystyle f\left( x \right)=3{{x}^{4}}-5{{x}^{3}}+2{{x}^{2}}+4\text{ at }x=2.$

Topic: Evaluation of Polynomials

None

12.

Divide $ \displaystyle 2{{x}^{4}}-3{{x}^{3}}+4{{x}^{2}}-5\text{ by }x-2$ using synthetic division and find the remainder.

Topic: Synthetic Division of Polynomials

–1

None

13.

If$ \displaystyle f\left( x \right)={{x}^{3}}-6{{x}^{2}}+11x-6,$ find $ \displaystyle f\left( 3 \right)$ using the Remainder Theorem.

Topic: Remainder theorem

None

14.

Factor the polynomial $ \displaystyle f\left( x \right)=2{{x}^{3}}-4{{x}^{2}}-6x.$

Topic: Factorization of polynomials

$ \displaystyle 2x\left( {x-3} \right)\left( {x+1} \right)$

$ \displaystyle 2x\left( {x+3} \right)\left( {x-1} \right)$

$ \displaystyle 2x\left( {x-1} \right)\left( {x+3} \right)$

$ \displaystyle 2x\left( {x+1} \right)\left( {x-3} \right)$

None

15.

Divide the polynomial $ \displaystyle 6{{x}^{3}}-5{{x}^{2}}+2x-1$ by $ \displaystyle 2x-1$ and find the quotient and remainder

Topic: Polynomial Division

Quotient: $ \displaystyle 3{{x}^{2}}-x+\dfrac{1}{2}$, Remainder: $ \displaystyle \dfrac{{-1}}{2}$

Quotient: $ \displaystyle 3{{x}^{2}}-x+2$, Remainder: 1

Quotient: $ \displaystyle 3{{x}^{2}}-2x+3$, Remainder: 0

Quotient: $ \displaystyle 3{{x}^{2}}+x-1$, Remainder: 2

None

1 out of 15

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Class 9 Practice Level 3 – Polynomials – set – 2

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