Question
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Answer
\(2x^{2}-9x-11 = (x+1)(2x-11)\)
Solution
Factor the expression \( 2x^2-9x-11 \).
Factor the expression by following steps:
- step0: Factor:
\(2x^{2}-9x-11\)
- step1: Rewrite the expression:
\(2x^{2}+\left(-11+2\right)x-11\)
- step2: Calculate:
\(2x^{2}-11x+2x-11\)
- step3: Rewrite the expression:
\(x\times 2x-x\times 11+2x-11\)
- step4: Factor the expression:
\(x\left(2x-11\right)+2x-11\)
- step5: Factor the expression:
\(\left(x+1\right)\left(2x-11\right)\)
The factored form of the expression \(2x^{2}-9x-11\) is \((x+1)(2x-11)\).
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Simplify this solution Extra Insights
To factor the quadratic \( 2x^2 - 9x - 11 \), we first look for two numbers that multiply to \( 2 \times -11 = -22 \) and add to \( -9 \). The numbers that satisfy this condition are \( -11 \) and \( 2 \). Rewrite the middle term: \[ 2x^2 - 11x + 2x - 11 \] Next, we group the terms: \[ (2x^2 - 11x) + (2x - 11) \] Factor out common terms: \[ x(2x - 11) + 1(2x - 11) \] Now factor by grouping: \[ (2x - 11)(x + 1) \] So the factored form of \( 2x^2 - 9x - 11 \) is \( (2x - 11)(x + 1) \).
