Pregunta
\( 1<\quad \) Factor out the greatest common factor from the following polynomial \[ 5 x\left(7 x^{4}+6\right)-2\left(7 x^{4}+6\right) \]
Ask by Gross Ayala. in the United States
Mar 10,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The polynomial factors to \((7x^4 + 6)(5x - 2)\).
Solución
1. Observe that both terms in the polynomial
\[
5 x\left(7 x^{4}+6\right)-2\left(7 x^{4}+6\right)
\]
share the common factor \(\left(7 x^{4}+6\right)\).
2. Factor out \(\left(7 x^{4}+6\right)\) from each term:
\[
\left(7 x^{4}+6\right)(5x - 2).
\]
3. The factored form of the polynomial is:
\[
\left(7 x^{4}+6\right)(5x-2).
\]
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Simplifique esta solución Mind Expander
To factor out the greatest common factor, we first identify the common expression in both terms of the polynomial. Notice that both terms include the expression \( (7x^4 + 6) \). We can factor it out: \[ 5x(7x^4 + 6) - 2(7x^4 + 6) = (7x^4 + 6)(5x - 2) \] So, the factored form of the polynomial is: \[ (7x^4 + 6)(5x - 2) \]
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