Question

If x – 2 is a factor of polynomial p(x) = x2 – 8x –a, then find the value of a and the other

factors of p(x) .​

Answer 1

Answer:

p(x)=(x-6) (x-2)

Step-by-step explanation:

x – 2 is a factor of polynomial

p(x) = x² – 8x –a

so p(2)=0

p(2)=2²-8*2-a=0

4-16-a=0

a=-12

So p(x)=x² – 8x +12

x²-6x-2x+12

x(x-6)-2(x-6)

p(x)=(x-6) (x-2)

Answer 2

Step-by-step explanation:

Given polynomial p(x)=x²-8x-a

given factor of p(x)= (x-2)

By the factor theorem if (x-2) is a factor of p(x) then p(2)=0

=>p(2)=2²-8(2)-a=0

=>4-16-a=0

=>-12-a=0

=>-a=12

=>a= -12

The value of a =-12

The resultant polynomial =x²-8x+12

=>x²-2x-6x+12

=>x(x-2)-6(x-2)

=>(x-2)(x-6)

The other factor =(x-6)

Factor theorem:-

Let p(x) be a polynomial and (x-a) is a factor if p(a)=0 vice versa