Question

How do you factor the trinomial `x^2 + 14x + 49`?

Answer 1

`(x+7)^2`

Explanation:

Suppose we have the variables 'a' and 'b' where

`ab=49`
`a+b=14`

Note that this approach only works if the coefficient of `x^2` is 1.
That is: `x^2 -= 1 times x^2color(white)(xxxxxx) ( or 1x)`

`7 times 7 =49`
`7+7 =14`

So we have:

`(x+7)(x+7) -= (x+7)^2`

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Foot note for reference:
`(x+7)(x+7) " is the same as " x(x+7) + 7(x+7)`