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Answer
The expression \(5x^{2}-9x+4\) factors to \((x-1)(5x-4)\).
Solution
Factor the expression \( 5x^2-9x+4 \).
Factor the expression by following steps:
- step0: Factor:
\(5x^{2}-9x+4\)
- step1: Rewrite the expression:
\(5x^{2}+\left(-4-5\right)x+4\)
- step2: Calculate:
\(5x^{2}-4x-5x+4\)
- step3: Rewrite the expression:
\(x\times 5x-x\times 4-5x+4\)
- step4: Factor the expression:
\(x\left(5x-4\right)-\left(5x-4\right)\)
- step5: Factor the expression:
\(\left(x-1\right)\left(5x-4\right)\)
The factored form of the expression \(5x^{2}-9x+4\) is \((x-1)(5x-4)\).
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Simplify this solution Extra Insights
To factor the quadratic expression \( 5x^2 - 9x + 4 \), we can start by identifying two numbers that multiply to \( 5 \times 4 = 20 \) (the product of the coefficient of \( x^2 \) and the constant term) and add up to \( -9 \) (the coefficient of \( x \)). The numbers that work are \( -5 \) and \( -4 \). We can rewrite the middle term as: \[ 5x^2 - 5x - 4x + 4. \] Next, we group the terms: \[ (5x^2 - 5x) + (-4x + 4). \] Now we factor by grouping: \[ 5x(x - 1) - 4(x - 1). \] This gives us: \[ (5x - 4)(x - 1). \] So, the completely factored form of \( 5x^2 - 9x + 4 \) is: \[ (5x - 4)(x - 1). \]
