Class 9 Quiz Level 3 (Difficult) – Polynomials

Total questions: 10

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

Topic: Degree of Polynomials

Deselect Answer

None

Using the remainder theorem, find the remainder when 2$ \displaystyle x$³ + 3$ \displaystyle x$² – 5$ \displaystyle x$ + 7 is divided by $ \displaystyle x$ – 2.

Topic: Remainder theorem

Deselect Answer

None

Divide $ \displaystyle 2{{x}^{3}}+5{{x}^{2}}-4x-7\ \text{by }x+2$ and find the quotient.

Topic: Division of polynomials

Deselect Answer

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

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

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

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

None

Divide $ \displaystyle 4{{x}^{3}}+6{{x}^{2}}-2x-3\ \text{by 2}x-1.$ What is the quotient?

Topic: Polynomial long Division

Deselect Answer

$ \displaystyle 2{{x}^{2}}+5x+1$

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

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

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

None

Factorize the polynomial $ \displaystyle x$³ + 4$ \displaystyle x$² – 3$ \displaystyle x$ – 18 completely given that $ \displaystyle x$ = –3 is a root.

Topic: Factorization

Deselect Answer

$ \displaystyle (x\text{ }+\text{ }3)({{x}^{2}}+x-6)$

$ \displaystyle (x\text{ }-\text{ }3)({{x}^{2}}+6x-1)$

$ \displaystyle (x\text{ }+2)({{x}^{2}}+2x-9)$

$ \displaystyle (x\text{ }+3)({{x}^{2}}+6x+6)$

None

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

Deselect Answer

$ \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

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

Topic: Polynomial Equations

Deselect Answer

$ \displaystyle x=-1$

$ \displaystyle x=-3$

$ \displaystyle x=0$

$ \displaystyle x=1$

None

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

Deselect Answer

–1

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

Deselect Answer

–11

–7

None

10.

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

Topic: Factorization of polynomials

Deselect Answer

$ \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

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Class 9 Quiz Level 3 (Difficult) – Polynomials

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