Simplify:(p – 2)(p + 1)(p – 4)

1.	Simplify:(p – 2)(p + 1)(p – 4)
Answer» (p – 2)(p + 1)(p – 4) = (p + (-2))0 +1)(p + (-4)) Comparing (p – 2) (p + 1) (p – 4) with (x + a) (x + b) (x + c) we have x = p ; a = -2; b = 1 ; c = -4. (x + a) (x + b) (x + c) = x³ + (a + b + c) x² + (ab + be + ca) x + abc = p³ + (-2 + 1 + (-4))p² + ((-2) (1) + (1) (-4) (-4) (-2)p + (-2) (1) (-4) = p³ + (-5 )p² + (-2 + (-4) + 8)p + 8 = p³ – 5p² + 2p + 8

Answer»

(p – 2)(p + 1)(p – 4) = (p + (-2))0 +1)(p + (-4))

Comparing (p – 2) (p + 1) (p – 4) with (x + a) (x + b) (x + c) we have x = p ; a = -2; b = 1 ; c = -4.

(x + a) (x + b) (x + c) = x³ + (a + b + c) x² + (ab + be + ca) x + abc

= p³ + (-2 + 1 + (-4))p² + ((-2) (1) + (1) (-4) (-4) (-2)p + (-2) (1) (-4)

= p³ + (-5 )p² + (-2 + (-4) + 8)p + 8

= p³ – 5p² + 2p + 8

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