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Question
Factorise the expression and divide them as directed:
(2x3 – 12x2 + 16x) ÷ (x – 2)(x – 4)
Solution
We have,
(2x3 – 12x2 + 16x) ÷ (x – 2)(x – 4)
= `(2x^3 - 12x^2 + 16x)/((x - 2)(x - 4))`
= `(2x(x^2 - 6x + 8))/((x - 2)(x - 4))`
= `(2x(x^2 - 4x - 2x + 8))/((x - 2)(x - 4))`
= `(2x[x(x - 4) - 2(x - 4)])/((x - 2)(x - 4))`
= `(2x(x - 4)(x - 2))/((x - 2)(x - 4))`
= 2x
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