Question

for what value of k is the polynomial p(x)=2x³–kx²+3x+10 exactly divisible by (x–2)​

Answer 1

Answer:

k= 0

Step-by-step explanation:

x - 2=0

x=2

putting value of x

16-4k+6+10=0

16 - 16 -4k=0

-4k=0

k=0

Answer 2

$\large{\mathbb{\purple{\boxed{\green{\underbrace{\overbrace{\red{\boxed{\green{♪Answer♪}}}}}}}}}}$

★ x - 2 = 0

★ x = 2

Putting the value of x in P(X) :-

P(x) = 2x³– kx²+ 3x + 10 = 0

P(2) = 2(2)³ - k(2)² + 3(2) + 10 = 0

=> 2(8) + k(4) + 6 + 10 = 0

=> 16 + 4k + 6 + 10 = 0

=> 4k + 32 = 0

=> 4k = (-32)

=> k = $\dfrac{\cancel{(-32)}}{\cancel{4}}$

$\huge{\boxed{\orange{K\:=\:(-8)}}}$