Question

If (x+5) is a factor of P(x)= x^3 -20x + 5k then find the value of k?​

Answer 1

Answer:

The value of k = 5

Step-by-step explanation:

Since it is given that (x + 5) is a factor, by applying Factor theorem,

(x + 5) = 0

→ x = 0 - 5

→ x = -5

Put this value of x in the given polynomial p(x) and then equate that polynomial to 0.

p(x) = x³ - 20x + 5k

p(-5) = (-5)³ - 20(-5) + 5k = 0

⇒ p(-5) = -125 + 100 + 5k = 0

⇒ p(-5) = 5k - 25 = 0

⇒ 5k - 25 = 0

⇒ 5k = 25

⇒ k = 25 ÷ 5

⇒ k = 5

∴ k = 5