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Question

Factorise x45x2+4 using factor theorem

A
f(x)=(x-1)(x+1)(x-2)(x+2)
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B
f(x)=(x-1)(x+1)(x-3)(x+3)
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C
f(x)=(x-2)(x+2)(x-3)(x+3)
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D
f(x)=(x-5)(x+5)(x-3)(x+3 )
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Solution

The correct option is A f(x)=(x-1)(x+1)(x-2)(x+2)
Let f(x)=x45x2+4
factors of 4 = ±1,±2,±4
f(1)=(1)45(1)2+4=15+4=0
f(1)=(1)45(1)2+4=15+4=0
f(2)=(2)45(2)2+4=1620+4
f(2)=0
f(2)=(2)45(2)2+4=1620+4
f(2)=0
f(4)=(4)45(4)2+4=25680+4
=1800
f(4)=(4)45(4)2+4=1800

By fator theorem,
(x-1), (x+1), (x-2) and (x+2) are factors of f(x).
So, f(x)=(x-1)(x+1)(x-2)(x+2)

Thus, the correct answer is option (a).

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