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Factor completely: 4x^3 - 49x

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To factor the expression
\displaystyle\sf 4x^3 - 49x, we can first identify that it is a polynomial with two terms. Notice that both terms have a common factor of
\displaystyle\sf x. Factoring out
\displaystyle\sf x, we have:


\displaystyle\sf x(4x^2 - 49).

Now, we can observe that the expression
\displaystyle\sf 4x^2 - 49 is a difference of squares. It can be rewritten as
\displaystyle\sf (2x)^2 - 7^2. Applying the formula for factoring a difference of squares, we obtain:


\displaystyle\sf x(2x + 7)(2x - 7).

Therefore, the completely factored form of
\displaystyle\sf 4x^3 - 49x is
\displaystyle\sf x(2x + 7)(2x - 7).

User Gueorgui Obregon
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