Question

If the polynomial 3x³+kx²+2x-3 leaves a remainder 5 when divided by x-2, find the value of k, using remainder theorem.

Answer 1

Answer:

k = - 5

Step-by-step explanation:

Answer 2

Answer :-

-5

Explanation :-

Given :

Polynomial 3x³ + kx² + 2x - 3 leaves a remainder 5

To Find :

The value of k.

Solution :

x - 2 =0

x = 2

So,value of x is equal to 4.

$\sf{}Let\ f(x)=3x^3+kx^2+2x-3$

$\sf{}[putting\ x= 2]$

$\Rightarrow \sf{} f(2)=3(2)^3+k(2)^2+2(2)-3$

$\Rightarrow \sf{} 5=3(8)+k(4)+4-3$

$\Rightarrow \sf{}5=25+4k$

$\Rightarrow \sf{}5-25=4k$

$\Rightarrow \sf{} -20=4k$

$\Rightarrow \sf{} -\dfrac{20}{4}=k$

$\Rightarrow \sf{} -5=k$

Therefore,the value of k = -5