(i) x2 + 5x + 4 = x2 + (1 + 4)x + (1 x 4)
Which is of the form x2 + (a + b)x + ab
= (x + a) (x + b)
x2 + (1 + 4)x + (1 x 4) = (x + 1) (x + 4)
∴ x2 + 5x + 4 = (x + 1) (x + 4)
(ii) x2 – 5x + 4 = x2 + ((-1) + (- 4))x + (-1) (- 4)
Which is of the form x2 + (a + b)x + ab
= (x + a) (x + b)
x2 + ((-1) + 4))x + ((-1)(-4)) = (x + (-4))
= (x – 1) (x – 4)
x2 – 5x + 4 = (x – 1) (x – 4)