Factorize completely: (x^{2} + x^{2}y + 3x – 10y + 3xy – 10).

Correct Answer: Option C

Explanation

(x^{2} + x^{2}y + 3x – 10y + 3xy -10)

= (x^{2} + x^{2}y + 3x + 3xy – 10y – 10  = x^{2}(1 + y) + 3x(1 + y) – 10(y + 1))

= ((x^{2} + 3x – 10)(y + 1))

= ((x^{2} + 3x – 10) = x^{2} – 2x + 5x – 10)

= (x(x – 2) + 5(x – 2) = (x – 2)(x +5))

(therefore x^{2} + x^{2}y + 3x – 10y + 3xy -10 = (x – 2)(x + 5)(y + 1)).