Polynomials Questions and answers

  1. Elementary Mathematics
    1. Quadratic Equations
    2. Simplification
    3. Area and perimeter
    4. Volume and surface area
    5. Geometry
    6. Trigonometry
    7. Polynomials
    8. Height and Distance
    9. Simple and Decimal fraction
    10. Indices and Surd
    11. Logarithms
    12. Trigonometric ratio
    13. Straight lines
    14. Triangle
    15. Circles
    16. Quadrilateral and parallelogram
    17. Loci and concurrency
    18. Statistics
    19. Rectangular and Cartesian products
    20. Rational expression
    21. Set theory
    22. Factorisation
    23. LCM and HCF
    24. Clocks
    25. Real Analysis
21). Factors of \( \Large 12x^{2}+11x+2 \) are
A). \( \Large \left(3x+2\right) \left(4x+1\right) \)
B). \( \Large \left(3x-2\right) \left(4x-1\right) \)
C). \( \Large \left(4x+2\right) \left(3x+1\right) \)
D). \( \Large \left(x+3\right) \left(x-4\right) \left(x-1\right) \)
22). H.C.F. of the polynomials \( \Large 2x^{3}-3x^{2}-11x+6\ and\ 2x^{2}+x-1 \) is
A). \( \Large 3x-1 \)
B). \( \Large 2x-1 \)
C). \( \Large x - \frac{1}{2} \)
D). \( \Large 2x-5 \)
23). L.C.M. of \( \Large x^{4}+x^{2}+1,\ x^{4}-x^{2}-2x-1,\ x^{6}-1 \) is
A). \( \Large \left(x^{6}+1\right) \left(x^{4}+x^{2}+1\right) \)
B). \( \Large \left(x^{6}-1\right) \left(x^{2}+x+1\right) \)
C). \( \Large \left(x^{6}+1\right) \left(x^{2}-x-1\right) \)
D). \( \Large \left(x^{6}-1\right) \left(x^{2}-x-1\right) \)
24). If a four-digited perfect square number is such that the number formed by the first two digits and the number formed by the last two digits are also perfect squares; then four-digited number is
A). 6416
B). 3616
C). 1681
D). 1664
25). If \( \Large x^{9}-3 \) is divided by \( \Large x^{3}-1 \), then the remainder will be
A). 2
B). -2
C). 1
D). -1


26). When \( \Large x^{4}+4x^{3}+3x^{2}+2 \) is divided by \( \Large x^{2}+2x \), then the remainder is.
A). \( \Large 2x+2 \)
B). \( \Large 2x+3 \)
C). \( \Large x+4 \)
D). \( \Large -x+5 \)
27). If \( \Large a-b=1 \), then value of\( \Large a^{3}-b^{3}+3ab \) will be
A). -3
B). -1
C). 1
D). 3
28). If \( \Large x-3 \) is a factor of \( \Large x^{2}+kx+9 \), then value of k is
A). 6
B). -6
C). 3
D). -3
29). Factors of \( \Large ab \left(c^{2}+1\right)+c \left(a^{2}+b^{2}\right) \) are
A). \( \Large \left(a+bc\right)\ and\ \left(b+ca\right) \)
B). \( \Large \left(ca+b\right)\ and\ \left(ab+c\right) \)
C). \( \Large \left(ab+c\right)\ and\ \left(bc+a\right) \)
D). \( \Large \left(ab-c\right)\ and\ \left(bc-a\right) \)
30). Factors of \( \Large \left(2x-3y\right)^{3}+ \left(3y-5z\right)^{3}+ \left(5z-2x\right)^{3} \) are
A). \( \Large 3 \left(2x-3y\right) \left(3y-5z\right) \left(5z-2x\right) \)
B). \( \Large 3 \left(3x-2y\right) \left(3y-5z\right) \left(5z-2x\right) \)
C). \( \Large 3 \left(2x-3y\right) \left(5y-3z\right) \left(5z-2x\right) \)
D). \( \Large 3 \left(2x-3y\right) \left(3y-5z\right) \left(2z-5x\right) \)
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