Question

what property do we use to check that our factored form is equivalent to the standard form

Answer 1

Lets solve an example:

$\begin{gathered} y=x^2+6x+8 \\ \end{gathered}$

this quadratic polynomial is in standard form. We can write the same polynomial in factored form as

$y=(x+4)(x+2)$

In the case of quadratic polynomials, a fast check is

that is, 4 plus 2 must be equal to 6 in the term 6x and

4 times 2 must be 8 in the constant term, which is 8.