Question

If x3 - 5x2+kx-6 is divisible by x+3, then what is the value of k?

Answer 1

Answer:-

$\red{\bigstar}$$\large\boxed{\boxed{\rm\purple{k = -26}}}$

• Given:-

✧ $\sf{x^3 - 5x^2 + kx - 6}$ divisible by $\sf{x + 3}$

• To Find:-

✧ Value of k.

• Solution:-

Given that, $\sf{x^3 - 5x^2 + kx - 6}$ is divisible by $\sf{x + 3}$ therefore, $\sf{x+3}$ is zero of the given polynomial.

Hence,

✧ $\sf{x + 3 = 0}$

→ $\bf\pink{x = -3}$

• Substituting in the polynomial:-

✧ $\sf{x^3 - 5x^2 + kx - 6}$

→ $\sf{(-3)^3 - 5(-3)^2 + k(-3) - 6 = 0}$

→ $\sf{-27 - 5(9) - 3k - 6 = 0}$

→ $\sf{-27 - 45 - 3k - 6 = 0}$

→ $\sf{-78 - 3k = 0}$

→ $\sf{-3k = 78}$

→ $\sf{-k = \dfrac{78}{3}}$

→ $\sf{-k = 26}$

→ $\bf\pink{k = -26}$

Therefore, the value of k is -26.