Question

The expression x3 – kx2 + 14x -8 has a factor (x – 2).

i) find the value of k.

ii) with the value of k, factorise the above expression completely.​

Answer 1

Solution :-

since, (x - 2) is a factor of given expression x³ – kx² + 14x - 8 .

so,

→ f(2) = 0

then,

→ f(x) = x³ – kx² + 14x - 8

→ f(2) = (2)³ - k(2)² + 14*2 - 8

→ 8 - 4k + 28 - 8 = 0

→ 4k = 28

→ k = 7 .

then, dividing the expression by (x - 2) we get,

x - 2 ) x³ – 7x² + 14x - 8 ( x² - 5x + 4

x³ - 2x²

- 5x² + 14x

- 5x² + 10x

4x - 8

4x - 8

0

therefore,

→ x³ – kx² + 14x - 8

→ (x - 2)(x² - 5x + 4)

→ (x - 2)(x² - x - 4x + 4)

→ (x - 2){x(x - 1) - 4(x - 1)}

→ (x - 2)(x - 1)(x - 4)

→ (x - 1)(x - 2)(x - 4) (Ans.)

Learn more :-

solution of x minus Y is equal to 1 and 2 X + Y is equal to 8 by cross multiplication method

https://brainly.in/question/18828734

Answer 2

Answer:

i) k = 7

ii) (x-4) (x-1) (x-2) is the answer