how do you know if a trinominal is a perfect square ??????

Question

zepdrix · Answer

$$\Large\bf\sf x^2+bx+c$$

Is a perfect square when,$$\Large\bf\sf \left(\frac{b}{2}\right)^2\quad=\quad c$$

anonymous · Answer

can you explain it in words please?

zepdrix · Answer

Umm here's maybe an easier way to understand it.$$\Large\bf\sf (x+y)^2\quad=\quad (x+y)(x+y)$$Foiling it out gives us,$$\Large\bf\sf x^2+2xy+y^2$$When we expand out a square,
we get the `square of the first`,
`2 times the product of both`,
and the `square of the second`.

zepdrix · Answer

So if we have a polynomial, if we can write it as a square + a square + the product of both, then it's a perfect square.

Example:$$\Large\bf\sf x^2+6x+9$$Is a perfect square because we write it as,$$\Large\bf\sf x^2+2(3x)+3^2$$Square of the first, square of the second, and 2 times the product of both.

zepdrix · Answer

$$\Large\bf\sf =(x+3)^2$$

anonymous · Answer

thanks