Question
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Tutor-Verified Answer
Answer
The factored form is \( \frac{2}{5}x(1+5x) \).
Solution
Factor the expression \( 0.4x+2x^{2} \).
Factor the expression by following steps:
- step0: Factor:
\(0.4x+2x^{2}\)
- step1: Convert the expressions:
\(\frac{2}{5}x+2x^{2}\)
- step2: Factor the expression:
\(\frac{2}{5}\left(x+5x^{2}\right)\)
- step3: Factor the expression:
\(\frac{2}{5}x\left(1+5x\right)\)
The factored form of the expression \(0.4x + 2x^2\) is \(\frac{2}{5}x(1+5x)\).
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Simplify this solution Beyond the Answer
To factorise the expression \(0.4x + 2x^2\), you can first factor out the common term, which is \(x\). This gives you: \[x(2x + 0.4).\] Next, you can simplify \(0.4\) as \(\frac{2}{5}\) if you want to factor further. So the factored form can also be written as: \[x\left(2x + \frac{2}{5}\right).\] This is effectively the factorization, where you have extracted \(x\) as a common factor. To ensure you're completely in the clear, if you want to express it in a different format or further simplify, you could write: \[x\left(\frac{10x + 2}{5}\right).\] Now you have a neat expression that clearly shows the factors in play!
