Question

Find the remainder when x^3 -ax^2 +6x -a is divisible by x -a
Pls give right answer​

Answer 1

Answer:

5a

Step-by-step explanation:

Let's first find the zeros of the dividend g(x). In order to find the zeros of the g(x), we need to solve the equation g(x) = 0.

$\longmapsto\rm {g(x) = 0 }$

• g(x) or dividend is (x - a).

$\longmapsto\rm {x - a = 0 }$

Transposing -a from L.H.S to R.H.S. Its sign will get changed.

$\longmapsto\rm {x = 0 + a }$

Performing addition in R.H.S.

$\longmapsto\bf {x = a }$

Now, by the remainder theorem, as we know that when p(x) is divided by (x - a) ,then the remainder is p(a).

$\longmapsto\rm {p(a) = (a)^3 - a(a^2) + 6a - a }$

Simplifying further.

$\longmapsto\rm {p(a) = a^3 - a^3 + 5a }$

Performing subtraction.

$\longmapsto\bf {p(a) = 5a }$

∴ The remainder is 5a.

*For verification, refer to the attachment! We've verified it using long division method.