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
61). The value of \( \Large \frac{ \left(x-y\right)^{3}+ \left(y-z\right)^{3}+ \left(z-x\right)^{3} }{ \left(x^{2}-y^{2}\right)^{3}+ \left(y^{2}-z^{2}\right)^{3} \left(z^{2}-x^{2}\right)^{3} } \)
A). 1
B). \( \Large \left[ 2 \left(x+y+z\right) \right]^{-1} \)
C). \( \Large \left[ \left(x+y\right) \left(y+z\right) \left(z+x\right) \right]^{-1} \)
D). 0
62). If remainder of the polynomial \( \Large x^{3}+x^{2}+x+a \) when divided by \( \Large \left(x-2\right) \) is zero, then value of a is
A). -10
B). -12
C). -14
D). -16
63). If \( \Large \left(x+1\right) \) is a factor of \( \Large x^{4}+9x^{3}+7x^{2}+9ax+5a^{2} \), then
A). \( \Large a = \sqrt{137} \)
B). \( \Large 5a^{2}-9a-1=0 \)
C). \( \Large 5a^{2}-9a-17=0 \)
D). \( \Large a = \sqrt{131} \)
64). H.C.F. of the polynomials \( \Large x^{2}+3x+2 \) and \( \Large x^{3}+3x^{2}+3x+1 \) using Euclidean algorithm is
A). \( \Large x+4 \)
B). \( \Large 3x+2 \)
C). \( \Large 2x+1 \)
D). \( \Large x+1 \)
65). Let I, m and n be real dividing such that \( \Large l + m \ne n \). What is the quotient on dividing \( \Large l^{3}-m^{3}+n^{3}+3lmn \) by \( \Large \left(l-m+n\right) \)?
A). \( \Large l^{2}+m^{2}+n^{2}-lm-mn-ln \)
B). \( \Large l^{2}+m^{2}+n^{2}+lm+mn-ln \)
C). \( \Large l^{2}+m^{2}+n^{2}+lm+mn+ln \)
D). \( \Large l^{2}-m^{2}+n^{2}-lm-mn+ln \)


66). What is the. remainder when \( \Large x^{4}+1 \) is divided \( \Large x-2 \)?
A). 17
B). 15
C). 7
D). 1
67). If \( \Large x+y+z=0 \) and \( \Large xyz \ne 0 \), then what is the value of \( \Large \frac{1}{x^{2}+y^{2}-z^{2}}+\frac{1}{y^{2}+z^{2}-x^{2}}+\frac{1}{z^{2}+x^{2}-y^{2}} \)
A). 0
B). 1
C). -1
D). \( \Large \frac{1}{2} \)
68). For what value of p, is the coefficient of \( \Large x^{2} \) in the product \( \Large \left(2x-1\right) \left(x-k\right) \left(px+1\right) \) equal to 0 and the constant term equal to 2?
A). 2
B). \( \Large \frac{2}{5} \)
C). \( \Large \frac{5}{2} \)
D). 5
69). If m and n are natural numbers such that \( \Large 2^{m}-2^{n}=960 \), then what is the value of m?
A). 10
B). 12
C). 16
D). Cannot be determined
70). When \( \Large x^{3}+2x^{2}+4x+b \) is divided by \( \Large x+1 \), the quotient is \( \Large x^{2}+ax+3 \) and remainder is \( \Large -3 +2b \). What are the values of a and b respectively?
A). 1, 0
B). 0,1
C). 1, 1
D). -1, -1
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