Factorisation Questions and answers

  1. Elementary Mathematics
    1. Area and perimeter
    2. Circles
    3. Clocks
    4. Factorisation
    5. Geometry
    6. Height and Distance
    7. Indices and Surd
    8. LCM and HCF
    9. Loci and concurrency
    10. Logarithms
    11. Polynomials
    12. Quadratic Equations
    13. Quadrilateral and parallelogram
    14. Rational expression
    15. Real Analysis
    16. Rectangular and Cartesian products
    17. Set theory
    18. Simple and Decimal fraction
    19. Simplification
    20. Statistics
    21. Straight lines
    22. Triangle
    23. Trigonometric ratio
    24. Trigonometry
    25. Volume and surface area
1). If \( \Large a^{2}+b^{2}=24,\ ab=4 \) find the value of \( \Large \left(a-b\right) \)
A). 4
B). 6
C). 3
D). 2
2). If \( \Large x^{2}+\frac{1}{x^{2}}=38, \) find the value of \( \Large x-\frac{1}{x} \)
A). 8
B). 6
C). 4
D). 2
3). Simpllify: \( \Large \frac{a^{3}-b^{3}}{a^{2}+ab+b^{2}} \)
A). \( \Large \left(a + b\right) \)
B). \( \Large \left(a - b\right)^{2} \)
C). \( \Large \left(a - b\right) \)
D). \( \Large \left(a + b\right)^{2} \)
4). Find the factors of \( \Large x^{2}+10x+24 \)
A). \( \Large \left(x-6\right) \left(x-4\right) \)
B). \( \Large \left(x-6\right) \left(x+4\right) \)
C). \( \Large \left(x+6\right) \left(x-4\right) \)
D). \( \Large \left(x+6\right) \left(x+4\right) \)
5). Simplify \( \Large \frac{ \left(a^{3}+b^{3}\right) \left(a^{2}-b^{2}\right) }{ \left(a^{2}-ab+b^{2}\right) \left(a-b\right) } \)
A). \( \Large \left(a+b\right)^{2} \)
B). \( \Large \left(a-b\right)^{2} \)
C). \( \Large \left(a+b\right) \left(a-b\right) \)
D). None of these


6). Find the common factor of \( \Large x^{2}+\frac{1}{x^{2}}=102 \), then the value of \( \Large \left(x-\frac{1}{x}\right) \) is
A). 10
B). 12
C). 6
D). 4
7). Factorise: \( \Large x^{2}+18x+81 \)
A). \( \Large \left(x+9\right) \left(x-9\right) \)
B). \( \Large \left(x+9\right)^{2} \)
C). \( \Large \left(x+3\right)^{2} \)
D). \( \Large \left(x-9\right)^{2} \)
8). Simplify \( \Large \frac{ \left(x^{2}-4\right) \left(x^{3}-8\right) }{ \left(x-2\right)^{2} \left(x^{2}+2x+4\right) }=? \)
A). \( \Large \left(x-2\right)^{2} \)
B). \( \Large \left(x+2\right)^{2} \)
C). \( \Large \left(x+2\right) \)
D). \( \Large \left(x-2\right) \)
9). If a+b=5, ab=4 find the value of \( \Large a^{3}+b^{3} \)
A). 60
B). 50
C). 56
D). 65
10). Simplify \( \Large \frac{x^{2}+11x+30}{ \left(x^{2}+2x-15\right) } \)
A). \( \Large \frac{x+6}{x-3} \)
B). \( \Large \frac{x+3}{x-3} \)
C). \( \Large \frac{x+6}{x-5} \)
D). \( \Large \frac{x+5}{x+6} \)
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