Question

find the value of k so that (x-2) is a factor of 2x^3 - 6x^2 +5x+k

Answer 1

Answer:

k = -2

Step-by-step explanation:

Given, (x -2) is a factor of P(x) = 2x³ - 6x² + 5x + k

∴ (x - 2) = G(x)

G(x) = 0

x = 2

P(2) = 2(2)³ - 6(2)² + 5(2) + k

16 - 24 + 10 + k = 0

26 - 24 + k = 0

2 + k = 0

k = -2

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Answer 2

GIVEN:

(x - 2) is a factor of polynomial 2x³ - 6x² + 5x + k

TO FIND:

The value of k

SOLUTION:

x - 2 = 0

x = 2

p(x) = 0

Let p(x) = 2x³ - 6x² + 5x + k

We know that,

2x³ - 6x² + 5x + k = 0

Substitute p(2) in the polynomial to find the value of k.

p(2) = 2(2)³ - 6(2)² + 5(2) + k

= 2(8) - 6(4) + 10 + k

= 26 - 24 + k

0 = 2 + k

k = -2

Therefore, the value of k is -2.