Pregunta
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Respuesta verificada por el tutor
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\( 20x^{2}+24x-9 = (2x+3)(10x-3) \)
Solución
Factor the expression by following steps:
- step0: Factor:
\(20x^{2}+24x-9\)
- step1: Rewrite the expression:
\(20x^{2}+\left(-6+30\right)x-9\)
- step2: Calculate:
\(20x^{2}-6x+30x-9\)
- step3: Rewrite the expression:
\(2x\times 10x-2x\times 3+3\times 10x-3\times 3\)
- step4: Factor the expression:
\(2x\left(10x-3\right)+3\left(10x-3\right)\)
- step5: Factor the expression:
\(\left(2x+3\right)\left(10x-3\right)\)
The expression \( 20 x^{2}+24 x-9 \) can be factored as:
\[
(2x+3)(10x-3)
\]
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución The Deep Dive
To solve the quadratic equation \( 20 x^{2} + 24 x - 9 \), you can use the quadratic formula \( x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \), where \( a = 20 \), \( b = 24 \), and \( c = -9 \). Plugging in these values gives you a handy way to find the solutions and determine whether the roots are real or complex. Factoring this expression can be another challenge! You may want to look for a common factor or re-arrange to make grouped factoring easier. For instance, factor out the greatest common divisor where possible; in this case, you might notice that breaking the middle term (24x) could help in pairing the terms better for simpler factoring.
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