Question

Find the value of k if x-2 is a factor of 2x3 -6x2 +5x +k.

Answer 1

Step-by-step explanation:

Here given: x - 2 is a factor

and p(x)=x^3 - 6x^2 + 5x + k

=>x - 2 = 0

=>x = 2

put the value of x in p(x).

=> (2)^3 - 6(2)^2 + 5(2) + k = 0

=>8 - 24 + 10 + k = 0

=>k = 24 - 18

=>k = 6

Answer 2

Answer:

value of k = -2

Step-by-step explanation:

let the given given polynomial be denoted as :

p(x) = 2x³ - 6x² + 5x + k

(x - 2) is a factor of above polynomial:

so x - 2 = 0

x = 2

so p(2) = 0

substitute value of x = 2 in p(x)

(2)(2³) - (6)(2²) + (5)(2) + k = 0

(2)(2)(2)(2) - (6)(2)(2) + (5)(2) + k = 0

16 - 24 + 10 + k = 0

26 - 24 + k = 0

2 + k = 0

k = - 2

value of k = -2