Can we factorize the following expressions using any basic identities?

1.	Can we factorize the following expressions using any basic identities? Justify your answer.(i) x2 + 5x + 4(ii) x2 – 5x + 4
Answer» (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)

Can we factorize the following expressions using any basic identities? Justify your answer.(i) x2 + 5x + 4(ii) x2 – 5x + 4

Answer»

(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)