Pregunta
Factor the following expressior \[ \begin{array}{l}7 x^{2}+15 x+2 \\ ([?] x+[])(x+[])\end{array} \]
Ask by Chan Lambert. in the United States
Feb 20,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
La expresión \( 7x^{2}+15x+2 \) se factoriza como \( (7x+1)(x+2) \).
Solución
Factor the expression by following steps:
- step0: Factor:
\(7x^{2}+15x+2\)
- step1: Rewrite the expression:
\(7x^{2}+\left(1+14\right)x+2\)
- step2: Calculate:
\(7x^{2}+x+14x+2\)
- step3: Rewrite the expression:
\(x\times 7x+x+2\times 7x+2\)
- step4: Factor the expression:
\(x\left(7x+1\right)+2\left(7x+1\right)\)
- step5: Factor the expression:
\(\left(x+2\right)\left(7x+1\right)\)
La expresión \( 7 x^{2}+15 x+2 \) se puede factorizar como:
\[
(7x+1)(x+2)
\]
Por lo tanto, la factorización es:
\[
([7] x+[1])(x+[2])
\]
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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The Deep Dive
To factor the expression \( 7x^2 + 15x + 2 \), we can look for two binomials whose outer and inner products give us the middle term when combined. We have: \[ (7x + 1)(x + 2) \] When expanded, this yields: \[ 7x^2 + 14x + 1x + 2 = 7x^2 + 15x + 2, \] confirming that our factorization is correct! So, filling in the brackets, we see the factorization as: \[ (7x+1)(x+2) \]
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