Question

x -a is a factor p(x) =x^6 -ax^5+x^4-ax^3+3x-a+2 find the value of a​

Answer 1

Answer:

a= -1

Step-by-step explanation:

If (x-a) is a factor of

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

from remainder theorem,on putting x=a,the polynomial becomes zero.

$p(a) = 0 \\ \\ p(a) = {a}^{6} - a {a}^{5} + {a}^{4} - a {a}^{3} + 3a - a + 2 = 0 \\ \\ {a}^{6} - {a}^{6} + {a}^{4} - {a}^{4} + 3a - a + 2 = 0 \\ \\ 3a - a + 2 = 0 \\ \\ 2a + 2 = 0 \\ \\ 2a = - 2 \\ \\ a = \frac{ - 2}{2} \\ \\ a = - 1$

Hope it helps you.