Question

H-C.F of x^2+3x+ 2, x² + 5x+4 is​

Answer 1

Answer :-

Let's first find factors of the given two expression :-

→ x² + 3x + 2

Using the middle term splitting method :-

→ x² + 2x + x + 2

→ x ( x + 2 ) + 1 ( x + 2 )

→ ( x + 1 ) ( x + 2 )

x² + 3x + 2 = ( x + 1 ) ( x + 2 )

→ x² + 5x + 4

Using the middle term splitting method :-

→ x² + x + 4x + 4

→ x ( x + 1 ) + 4 ( x + 1 )

→ ( x + 4 ) ( x + 1 )

x² + 5x + 4 = ( x + 4 ) ( x + 1 )

Common factors of x² + 3x + 2 and x² + 5x + 4 is ( x + 1 )

Hence, HCF of x² + 3x + 2 and x² + 5x + 4 = x + 1