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Answer
The expression \(5x^{2}-3x-2\) factors to \((x-1)(5x+2)\).
Solution
Factor the expression \( 5x^2-3x-2 \).
Factor the expression by following steps:
- step0: Factor:
\(5x^{2}-3x-2\)
- step1: Rewrite the expression:
\(5x^{2}+\left(2-5\right)x-2\)
- step2: Calculate:
\(5x^{2}+2x-5x-2\)
- step3: Rewrite the expression:
\(x\times 5x+x\times 2-5x-2\)
- step4: Factor the expression:
\(x\left(5x+2\right)-\left(5x+2\right)\)
- step5: Factor the expression:
\(\left(x-1\right)\left(5x+2\right)\)
The factored form of the expression \(5x^{2}-3x-2\) is \((x-1)(5x+2)\).
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Simplify this solution Mind Expander
To factor the quadratic expression \( 5x^2 - 3x - 2 \) completely, we can use the method of grouping or trial and error. We need to find two numbers that multiply to \( 5 \times (-2) = -10 \) and add up to \(-3\). The numbers \(-5\) and \(2\) fit the bill, as \(-5 + 2 = -3\). Now we can rewrite the expression: \[ 5x^2 - 5x + 2x - 2 \] Next, we group the terms: \[ (5x^2 - 5x) + (2x - 2) \] Now factor out the common factors from each group: \[ 5x(x - 1) + 2(x - 1) \] Now we can factor out the common binomial factor \((x - 1)\): \[ (5x + 2)(x - 1) \] Thus, the completely factored form of \( 5x^2 - 3x - 2 \) is: \[ (5x + 2)(x - 1) \]
