Respuesta :
A trinomial is a polynomial with three terms.
FOr example:
[tex]4x^2+4x+6[/tex]The expression above has 3 terms, so it can be called a trinomial.
A perfect square trinomial is a trinomial that be factored into a binomial(a polynomial with 2 terms) and squared or multiply itself.
[tex](a+b)^2[/tex]Given the trinomial:
[tex]x^2+6x+9[/tex]Let's factor the trinomial:
[tex]\begin{gathered} x^2+6x+9 \\ \\ x^2+6x+3^2 \\ \text{Confirm the middle term is 2 times the product of the numbers being squared} \\ \text{ in the first and last terms.} \\ \\ 6x=2(3x) \\ \\ x^2+2(3x)+3^2 \end{gathered}[/tex]Take the perfect squaure trinomial rule: a² + 2ab + b² = (a + b)²
[tex](x+3)^2[/tex]Therefore, to identify a perfect square trinomial, the middle term must be two times the product of the numbers being squared in the first term and the last term.
ANSWER:
The middle term of the trinomial must be two times the product of the numbers being squared in the first term and the last term.
