Question

The value of a if (x-a) is a factor of the polynomial x^6-ax^5+x^4-ax^3+3x-a+2

Answer 1

Answer:

The answer is $a=-1$

Step-by-step explanation:

Factor theorem : (x-a) is a factor of polynomial P(x), then P(a)=0

Here $x-a$ is a factor of $P(x)=x^6-ax^5+x^4-ax^3+3x-a+2$

        $\Rightarrow P(a)=0\\\Rightarrow a^6-a(a^5)+a^4-a(a^3)+3a-a+2=0\\\Rightarrow a^6-a^6+a^4-a^4+2a+2=0\\\Rightarrow 2x+2=0\\\Rightarrow 2a=-2\\\Rightarrow a=-1$