Apartial factorization of x2-3x-10 is modeled with algebra tiles

X² - 3x - 10

x² = x * x

10 can be factored:

1 x 10 ⇒⇒⇒ difference between factors = 9

2 x 5   ⇒⇒⇒ difference between factors = 3  ⇒ (The correct pair)

(x-5)(x+2) = x(x+2) - 5(x+2)

                = x² + 2x - 5x - 10

                = x² - 3x - 10

∴ x - 5 = 0  ⇒⇒⇒ x = 5

  x + 2 = 0  ⇒⇒⇒ x = -2