Question

Question #bd0e0

Answer 1

You can't. This expression is unfactorable.

Explanation:

A perfect square trinomial is a trinomial (a polynomial with three terms) that can be factored down into one of two forms:

1) `(a+b)^2`

or

2) `(a-b)^2`

If we expand both of those out, we get

1) `(a+b)^2=a^2+2ab+b^2`

and

2) `(a-b)^2=a^2-2ab+b^2`

Let's see if `x^2-7x+49` is a perfect square trinomial. According to the expansion, we see that the first and last term have to be perfect squares. Let's check that:

`x^2` and `49` are the first and last term, respectively.

`sqrt(x^2)=x` and `sqrt(49)=+-7`

The two terms are perfect squares! Now let's see - the middle term has to be twice the product of the two squares.

Our two squares are `x` and `+-7` (NOTE: We have two different combinations for `+-7`: `+7` and `-7`, so we have to test both of them to see if they fit the properties of the middle term of a perfect square term).

`(2)(x)(+7)=14x`

Nope. Let's try the other combination:

`(2)(x)(-7)=-14x`

Nope either. Even though our first and last terms were perfect squares, the middle term did not have the properties of a perfect square trinomial.

Therefore, `x^2-7x+49` is not a perfect square trinomial. And so, it cannot be expressed as the product of two binomials.