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Question

Find the value of p for which x+1 is a factor of x4+(p−3)x3−(3p−5)x2+(2p−9)x+6. Also find the remaining factors for this value of p.

A
4;x2
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B
4;x1
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C
6;x3
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D
6;x+3
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Solution

The correct options are
A 4;x2
B 4;x1
Let f(x)=x4+(p3)x3(3p5)x2+(2p9)x+6.
Given x+1 is a factor of f(x), f(1)=0
p=4
Thus x4+x37x2x+6=(x+1)(x37x+6)
=(x+1)(x1)(x2+x6)
=(x+1)(x1)(x+3)(x2)
The other factors are x1,x2,x+3.

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