Question

find the value of a if (x-a) will divide x3-ax2+6-a​

Answer 1

Step-by-step explanation:

Given:-

(x-a) will divide x^3-ax^2+6-a

To find:-

Find the value of a ?

Solution:-

Given Polynomial = x^3-ax^2+6-a

P(x)=x^3-ax^2+6-a

Divisor = (x-a)

We know that

Factor theorem:-

P(x) is a polynomial is greater than or equal to 1 and (x-a) is another linear polynomial,If P(a)=0 then (x-a) is a factor of P(x).

=>P(a) = 0

=> (a)^3-a(a^2)+6-a = 0

=> a^3 - a^3 + 6 - a = 0

=> 0 + 6 - a = 0

=> 6 - a = 0

=> 6 = a

=> a = 6

Value of a = 6

Answer:-

The value of a for the given problem is 6

Used formula:-

Factor theorem:-

• P(x) is a polynomial is greater than or equal to 1 and (x-a) is another linear polynomial,If P(a)=0 then (x-a) is a factor of P(x).