Question

The value of $a$ if $(x-a)$ factor of $x^6-a{x}^5+x^4-a{x}^3+3x-a+2=0$ is

• A. a = 1
• B. a = -1
• C. a = 2
• D. a = -2

Answer 1

The correct option is B

a = -1

Consider $p\left(x\right)=x^6-a{x}^5+x^4-a{x}^3+3x-a+2$

If $(x-a)$ is a factor of $p\left(x\right)$, then $p\left(a\right)=0$.

$a^6-a(a{)}^5+a^4-a(a{)}^3+3\left(a\right)-a+2=0$.

$a^6-a^6+a^4-a^4+3a-a+2=0$.

$2a+2=0$

$a=-1$