Questions: Factor the expression completely. 5x-6x^2

Transcript text: Factor the expression completely. \[ 5 x-6 x^{2} \]

Solution

Solution Steps

Step 1: Identify the Greatest Common Factor (GCF)

The expression is \(5x - 6x^{2}\). The GCF of the terms \(5x\) and \(-6x^{2}\) is \(x\), since \(x\) is the highest power of \(x\) that divides both terms.

Step 2: Factor Out the GCF

Factor out \(x\) from the expression: \[ 5x - 6x^{2} = x(5 - 6x) \]

Step 3: Check for Further Factorization

The expression inside the parentheses, \(5 - 6x\), cannot be factored further since it is a linear expression with no common factors.

Final Answer

The completely factored form of the expression is: \[ \boxed{x(5 - 6x)} \]

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