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Factors of Algebraic Expressions and Factorisation

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Question

How do you factor the trinomial $100 x^{3} - 40 x^{2} + 4 x$ ?

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Solution

$100 x^{3} - 40 x^{2} + 4 x = 4 x (5 x - 1)^{2}$

Explanation:
All of the terms are divisible by $4 x,$ so separate that
out as a factor first.
$\begin{matrix} 100 x^{3} - 40 x^{2} + 4 x = 4 x (25 x^{2} - 10 x + 1) \end{matrix}$
The remaining quadratic factor is a perfect square
trinomial:
$25 x^{2} - 10 x + 1 = (5 x)^{2} - 2 (5 x) + 1^{2} = (5 x - 1)^{2}$
$S o$
$100 x^{3} - 40 x^{2} + 4 x = 4 x (5 x - 1)^{2}$

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Factors of Algebraic Expressions and Factorisation

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