3x² + kx + 4 is divisible by x - 1. The expression is also divisible by-

Question: 3x² + kx + 4 is divisible by x - 1. The expression is also divisible by-

Solution:
Given that
The expression 3x² + kx + 4 divisible by x - 1,
⇒ 3x² + kx + 4 = 0............(1)

Put x = 1 in equation (1)
⇒ 3 × 1² + k × 1 + 4 = 0
⇒ 3 + k + 4 = 0
⇒ k = - 7

Put the value k in equation (1)
⇒ 3x² - 7x + 4 = 0
⇒ 3x² - 3x - 4x + 4 = 0
⇒ 3x (x - 1) - 4(x – 1) = 0
⇒ (x - 1) (3x - 4) = 0

So, expression divisible by (x - 1) and (3x - 4).