Question
\( 1<\quad \) 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
Upstudy AI Solution
Tutor-Verified Answer
Answer
The polynomial factors to \((7x^4 + 6)(5x - 2)\).
Solution
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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Simplify this solution 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: \[ (7x^4 + 6)(5x - 2) \]
