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What are the components of (x6 – x4 – x5 – x4 + x2 - 4)?
- A(x - 1)
- B(x + 1)
- CBoth (x - 1) & (x + 1)
- DNeither (x - 1) or (x + 1)
Answer not set
Discussion 1
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CCommunity
As (x – 1) and (x + 1) are given in options, let us check by substituting x = 1 and x = - 1.
Substitute x = 1 in the given equation.
x6 – x4 – x5 – x4 + x2 – 4 = 16 – 14 – 15 – 14 + 12 – 4 = - 5
Hence, (x – 1) is not a factor of the given equation.
Now,
Substitute x = - 1in the given equation.
x6 – x4 – x5 – x4 + x2 – 4 = (- 1)6 – (- 1)4 – (- 1)5 – (- 1)4 + (- 1)2 – 4 = - 3
∴ Neither (x - 1) or (x + 1) are the components of (x6 – x4 – x5 – x4 + x2 - 4).
Substitute x = 1 in the given equation.
x6 – x4 – x5 – x4 + x2 – 4 = 16 – 14 – 15 – 14 + 12 – 4 = - 5
Hence, (x – 1) is not a factor of the given equation.
Now,
Substitute x = - 1in the given equation.
x6 – x4 – x5 – x4 + x2 – 4 = (- 1)6 – (- 1)4 – (- 1)5 – (- 1)4 + (- 1)2 – 4 = - 3
∴ Neither (x - 1) or (x + 1) are the components of (x6 – x4 – x5 – x4 + x2 - 4).