Question

Factorize the expressions and divide them as directed:

(i) (x² + 7x + 12) ÷ (x + 3)

(ii) (x² – 8x + 12) ÷ (x – 6)

Answer 1

(i) (x² + 7x + 12) ÷ (x + 3)

(x² + 7x + 12) ÷ (x + 3)

x² + 7x + 12 = x² + 3x + 4x + 12

= x(x + 3) + 4(x + 3)

= (x + 3) (x + 4)

(ii) (x² – 8x + 12) ÷ (x – 6)

(x² – 8x + 12) ÷ (x – 6)

x² – 8x + 12 = x² – 6x – 2x + 12

= x(x – 6) – 2(x – 6)

= (x – 6) (x – 2)

∴ (x² – 8x + 12) 4 (x – 6)

= ((x − 6)(x − 2))/(x − 6) = x – 2