Class 9 Practice Level 3 – Polynomials – set – 2 Leave a Comment / By anushka kumari / July 18, 2024 Class 9 Practice Level 3 – Polynomials – set – 2 Total questions: 15 1. 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 2. 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 3. Using the factor theorem, determine if $ \displaystyle {x-3}$ is a factor of $ \displaystyle {{x}^{4}}-81$. Topic: Factor Theorem Yes No Cannot determine Both None 4. 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 5. 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 1 3 None 6. Divide $ \displaystyle 3{{x}^{3}}+5{{x}^{2}}-2x+4\text{ by }x+2$ and find the remainder. Topic: Long Division of Polynomials 0 1 2 4 None 7. 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 8. 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 90 None 9. 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 0 –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 34 40 44 50 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 –1 5 19 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 0 6 8 10 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 Time's up
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