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Can we factorize the following expressions using any basic identities? Justify your answer.

(i) x2 + 5x + 4

(ii) x2 – 5x + 4

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Best 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)

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