Pregunta
Factor the trinomial: \[ 5 x^{2}+36 x+36 \] Answer \( \square \)
Ask by Peterson Ortega. in the United States
Mar 04,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The factored form is \((x+6)(5x+6)\).
Solución
Factor the expression \( 5x^2+36x+36 \).
Factor the expression by following steps:
- step0: Factor:
\(5x^{2}+36x+36\)
- step1: Rewrite the expression:
\(5x^{2}+\left(6+30\right)x+36\)
- step2: Calculate:
\(5x^{2}+6x+30x+36\)
- step3: Rewrite the expression:
\(x\times 5x+x\times 6+6\times 5x+6\times 6\)
- step4: Factor the expression:
\(x\left(5x+6\right)+6\left(5x+6\right)\)
- step5: Factor the expression:
\(\left(x+6\right)\left(5x+6\right)\)
The factored form of the trinomial \(5x^{2}+36x+36\) is \((x+6)(5x+6)\).
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg
Explicar 
Simplifique esta solución Beyond the Answer
To factor the trinomial \( 5x^{2} + 36x + 36 \), we can start by looking for two numbers that multiply to \( 5 \times 36 = 180 \) and add up to \( 36 \). The numbers \( 30 \) and \( 6 \) fit the bill since \( 30 + 6 = 36 \) and \( 30 \times 6 = 180 \). We can rewrite the middle term using these two numbers: \[ 5x^{2} + 30x + 6x + 36. \] Now, we can factor by grouping: \[ 5x(x + 6) + 6(x + 6) = (5x + 6)(x + 6). \] So, the factored form of the trinomial is: \[ \boxed{(5x + 6)(x + 6)} \] Feel free to double-check by expanding the factors!
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
