Question

The expression x² - y² + x + y - z² + 2yz - z has one factor, which is
1. y - x + z
2. x - y + z + 1
3. x + y - z + 1
4. x - y - z + 1

Answer 1

Correct Answer - Option 4 : x - y - z + 1

Given:

x2 - y2 + x + y - z2 + 2yz - z

Formula used:

(a - b)2 = a2 + b2 - 2ab

(a2 - b2) = (a - b)(a + b) 

Calculations:

Solving the given expression,

⇒ x2 - y2 + x + y - z2 + 2yz - z

⇒ x2 - (y2 + z2 - 2yz) + x + y - z

⇒ x2 - (y - z)² + x + y - z

⇒ (x - y - z)(x + y - z) + (x + y - z)

⇒ (x + y - z)(x - y - z + 1)

∴ Amongst the given options, x - y - z + 1 is one factor of the given expression