Question

Find the value of a if x–a is a factor of the polynomial

x6 –ax5 +x4 –ax3 + 3x2 –3ax + a –7​

Answer 1

Step-by-step explanation:

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

Answer 2

$\huge\bold\green{Answer☯}$

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

Thank you!!