Question

Factor completely: 4x^3 - 49x

Answer 1

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)`.