Question

If the polynomial p (x)= x-2x+3x-ax is divided by (x-2) it leaves a remainder 10 find the.value of



a.

Answer 1

When a polynomial $p(x)$ is divided by $x-a$, the remainder is $p(a)$. Here $p(x)=?$. p(x) is not clear.

Solve the equation $p(2)=10$ for a.

This gives the value of $a$

Answer 2

Given: Polynomial $p(x)=x-2x+3ax-ax$  is divided by $(x-2)$ it leaves a remainder $10.$

To find: Value of $a$ .

According to the remainder theorem, when a polynomial f(x) is divided by a linear polynomial x - b the remainder of that division will be equivalent to f(b).

So, if  $p(x)=x-2x+3ax-ax$  is divided by $(x-2),$

Then, $p(2)$ is the remainder

Then, $p(2)=10$

Now , $p(2)=2-2(2)+3a(2)-a(2)=10$

$\Rightarrow 2-4+6a-2a=10\\\\\Rightarrow\ -2+4a=10\\\\\Rightarrow\ 4a=12\\\\\Rightarrow a=\dfrac{12}{4}=3$

Hence, the value of $a$ is $3$ .