Question

if x+2 is a factor of a polynomial 5x^3+(k+2)x^2-3kx+2, then find the value of k.

Answer 1

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Answer 2

Given,

(x + 2) is a factor of the polynomial 5x³ + (k + 2)x² - 3kx + 2.

To find,

k.

Solution,

For any polynomial p(x), (x - a) is a factor of polynomial, if p(a) = 0.

It means the value of the variable obtained by equating the factor to zero must satisfy the polynomial equation p(x) = 0.

For the given polynomial, (x + 2) is a factor, so, the value of x can be found as,

x + 2 = 0

⇒ x = -2

Now, x = -2 should satisfy the equation p(x) = 0. So,

5(-2)³ + (k + 2)(-2)² - 3k(-2) + 2 = 0

⇒ 5(-8) + (k + 2)(4) + 6k + 2 = 0

⇒ -40 + 4k + 8 + 6k + 2 = 0

⇒ 10k - 40 + 10 = 0

⇒ 10k - 30 = 0

⇒ 10k = 30

⇒ k = 3.

Therefore, if (x + 2) is a factor of the given polynomial 5x³ + (k + 2)x² - 3kx + 2, then k = 3.