Find the product of the following:
(i) (x + 1) (x + 2) (x + 3)
(ii) (x – 2) (x – 3) (x + 4)
Answer :
(i) (x + 1) (x + 2) (x + 3)
It can be written as
= x3 + (1 + 2 + 3)x2 + (1 × 2 + 2 × 3 + 3 × 1) x + 1 × 2 × 3
By further calculation
= x3 + 6x2 + (2 + 6 + 3)x + 6
So we get
= x3 + 6x2 + 11x + 6
(ii) (x – 2) (x – 3) (x + 4)
It can be written as
= x3 + (- 2 – 3 + 4) x2 + [(-2) × (-3) + (-3) × 4 + 4 × (-2)]x + (-2) (-3) (4)
By further calculation
= x3 – x2 + (6 – 12 – 8)x + 24
= x3 – x2 – 14x + 24
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