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Question
Factorise the expressions and divide them as directed:
(x4 – 16) ÷ x3 + 2x2 + 4x + 8
Solution
We have,
(x4 – 16) ÷ x3 + 2x2 + 4x + 8
= `(x^4 - 16)/(x^3 + 2x^2 + 4x + 8)`
= `((x^2)^2 - 4^2)/(x^2(x + 2) + 4(x + 2))`
= `((x^2 + 4)(x^2 - 4))/((x^2 + 4)(x + 2))` ...[∵ a2 – b2 = (a + b)(a – b)]
= `(x^2 - 2^2)/(x + 2)`
= `((x + 2)(x - 2))/(x + 2)`
= x – 2
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