Question

Find the value of kif (x+2) is a factor of 3x3+kr2-18X+40. Hence, factorise the expression.​

Answer 1

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Answer 2

Answer:

k = - 13

Step-by-step explanation:

It is given that (x + 2) is a factor of 3x³ + kx² - 18x + 40.

By putting this factor equals to zero, we get the value of one of the zeroes of the above polynomial.

∴ (x + 2) = 0

x = - 2

f(x) = 3x³ + kx² - 18x + 40

Putting x = - 2, we get

→ f(- 2) = 3(- 2)³ + k(- 2)² - 18(- 2) + 40

→ f(- 2) = 3(- 8) + k(4) - 18(- 2) + 40

→ f(- 2) = - 24 + 4k + 36 + 40

→ f(- 2) = 4k - 24 + 36 + 40

→ f(- 2) = 4k - 24 + 76

→ f(- 2) = 4k + 52

Putting this equation equals to zero, so as to find the value of k.

→ 4k + 52 = 0

→ 4k = - 52

→ k = - 52 / 4

→ k = - 13