Find the value of a if x – a is a factor of the
polynomial
x
6
– ax5
+ x4
– ax3
+ 3x2
– 3ax + a – 7
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Answer:
Let p(x) is polynomial of x .
So, p(x) = x^6 - ax^5 + x^4 - ax^3 + 3x -a +2
Given (x-a) is factor of polynomial p(x)
x -a =0
So, x = a
Put x= a in p(x)
P(a) = a^6– a×a^5 + a^4 - a×a^3 + 3a - a +2
= a^6 - a^6 + a^4 - a^4 + 2a + 2
= 2a +2
Here ( x-a) is factor of given polynomial
So, remainder must be 0.
So, p(a) = 0
2a+2 = 0
Hence value of a = -1
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