How do you factor the perfect trinomial?

Answer 1

Do you mean some thing like 4x2 - 28xy + 49y2 ?

notice 4x2 = (2x)2 and 49y2 = either (7y)2 or (-7y)2 (1st and last terms must be squares) and the middle term is 2(2x)(-7y) (2 times sq root of 1st times sq root of last)

Once the pattern is recognized:

(sq root 1st + sqroot 2nd)2 or (sq root 1st - sqroot 2nd)2 depending on if middle term is positive or negative.

So, back to my example:

4x2 - 28xy + 49y2 = (2x - 7y)2 because middle is negative.

Simpler example factor x2 + 6x + 9. 1st and last are both squares

sq root of 9 = 3 3 times 2 = 6 that fits the middle

so x2 + 6x + 9 = (x + 3)2

Answer 2

Take a trinomial.

2x2 - 3x - 2

Factor it.

(2x + 1)(x - 2)

Repeat as necessary.

Answer 3

A factor is a number that divides evenly into another number with no remainder. 3 is a factor of 9. 4 is not a factor of 9.

Answer 4

2 x 3 = 6

(2,3) is a factor pair of 6.