Question

2. Explain how you identify a perfect square trinomial?

Answer 1

A trinomial is a polynomial with three terms.

FOr example:

`4x^2+4x+6`

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.

`(a+b)^2`

Given the trinomial:

`x^2+6x+9`

Let's factor the trinomial:

`\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}`

Take the perfect squaure trinomial rule: a² + 2ab + b² = (a + b)²

`(x+3)^2`

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.