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Algebraic Expressions, Identities and Factorisation — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSAlgebraic Expressions, Identities and Factorisation1 Mark
Question
Factorise the expressions and divide them as directed:
$\left(x^4-16\right) \div x^3+2 x^2+4 x+8$
✓

Answer

$\left(x^4-16\right) \div x^3+2 x^2+4 x+8$
We have,$=\frac{\text{x}^4-16}{\text{x}^3+2\text{x}+4\text{x}+8}$
$=\frac{({\text{x}^2})^2-4^2}{\text{x}^2(\text{x}+2)+4(\text{x}+2)} [\therefore\text{a}^2-\text{b}^2=(\text{a}+\text{b})(\text{a}-\text{b})]$
$=\frac{(\text{x}^2+4)(\text{x}^2-4)}{(\text{x}^2+4)(\text{x}+2)}$
$=\frac{\text{x}^2-2^2}{\text{x}+2}$
$=\frac{(\text{x}+2)(\text{x}-2)}{\text{x}+2}$
$=\text{x}-2$

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