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Question

Factorise
2x33x217x+30

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Solution

Let p(x)=2x33x217x+30
Constant term of p(x) = 30
Factors of 30 are ±1,±2,±3,±5,±6,±10,±15,±30
By trial, we find that p(2) = 0, so (x – 2) is a factor of p(x).
[2(2)33(2)217(2)+30=161234+30=0]
Now, we see that 2x33x217x+30

=(x2)(2x2+x15)
2x2+x15=2x(x+3)5(x+3) [By splitting the middle term]
=(x+3)(2x5)
2x33x217x+30=(x2)(x+3)(2x5)

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