Class 9 Quiz Level 3 (Difficult) – Polynomials Leave a Comment / By anushka kumari / October 17, 2024 Class 9 Quiz Level 3 (Difficult) – Polynomials Total questions: 10 1. 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 PolynomialsDeselect Answer 5 4 3 2 None 2. 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 1 3 5 7 None 3. 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 4. 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 5. Factorize the polynomial $ \displaystyle x$³ + 4$ \displaystyle x$² – 3$ \displaystyle x$ – 18 completely given that $ \displaystyle x$ = –3 is a root. Topic: FactorizationDeselect 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 6. 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 7. 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 8. 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 PolynomialsDeselect Answer 1 –1 5 19 None 9. Evaluate the polynomial $ \displaystyle p\left( x \right)=2{{x}^{3}}-3{{x}^{2}}+x-5\text{ at }x=-1.$ Topic: Evaluation of PolynomialsDeselect Answer –11 –7 1 3 None 10. Factor the polynomial $ \displaystyle f\left( x \right)=2{{x}^{3}}-4{{x}^{2}}-6x.$ Topic: Factorization of polynomialsDeselect 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 1 out of 10 Time's up
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