Question

if x cube minus 6 X square + 6 X + K is divided with x minus 3 then find k ​

Answer 1

right question - if x³ - 6x² + 6x + k is exactly divisible by x - 3, then find the value of k.

given :-

p(x) = x³ - 6x² + 6x + k

g(x) = x - 3

➡ x = 0 + 3

➡ x = 3

putting value of x in p(x)

➡ p(3) = (3)³ - 6(3)² + 6(3) + k = 0 (since the polynomial is exactly divisible by x - 3 so the remainder is 0)

➡ 27 - 54 + 18 + k = 0

➡ -27 + 18 + k = 0

➡ -9 + k = 0

➡ k = 9

hence, the value of k is = 9

Answer 2

Answer:

Value of k is 9

Step-by-step explanation:

Correction in your question:

If x³ - 6x² + 6x + k is exactly divisible by x - 3, then find the value of k.

Solution:

To Find:

Value of k

---------------------------

Method:

Given that,

(x -3) is a factor of the given polynomial.

So,

⇒( x-3) = 0

⇒x = 3

⇒p(x) = x³ - 6x² + 6x + k

⇒p(3) = (3)³ - 6 × (3)² + 6 × 3 + k

⇒27 - 6 × 9 + 18 + k

⇒ 27 - 54 + 18 + k = 0

⇒ 45 -54 + k = 0

⇒ k -9 = 0

⇒ k = 9

Hence, the value of k = 9