Pregunta
Factor the given polynomial by finding the greatest common monomial factor (or the negative of the \[ 14+14 x^{2} \]
Ask by Ryan Hobbs. in the United States
Feb 20,2025
Solución de inteligencia artificial de Upstudy
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The polynomial \(14+14x^{2}\) can be factored by taking out the greatest common monomial factor, which is 14. So, it becomes \(14(1+x^{2})\).
Solución
Factor the expression \( 14+14x^{2} \).
Factor the expression by following steps:
- step0: Factor:
\(14+14x^{2}\)
- step1: Factor the expression:
\(14\left(1+x^{2}\right)\)
The greatest common monomial factor of the given polynomial \(14+14x^{2}\) is \(14\). Therefore, the factored form of the polynomial is \(14(1+x^{2})\).
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Simplifique esta solución The Deep Dive
To factor the polynomial \( 14 + 14x^{2} \), we first identify the greatest common monomial factor. In this case, both terms share a common factor of 14. So, we can factor 14 out: \[ 14 + 14x^{2} = 14(1 + x^{2}) \] Now we have factored the polynomial into a product of the greatest common factor and the remaining expression. This form is particularly useful because it highlights how \( 14 \) can be easily scaled in any equation or application while examining the expression \( (1 + x^{2}) \) for its properties, such as its positivity over the reals.
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