Algebra Honors ( Period 4)

Factoring Trinomial Squares 8-9

Chapter 8-4 Déjà vu  Foil the following:

(a +3)² ( which is called a binomial squared)
(a + 3)(a +3) = a² + 3a + 3a + 9 = a² + 6a + 9 ( called a trinomial square)

Again, you see that the middle term is DOUBLE the product of the two terms in the binomial
and the first and last terms are simply the squares of each term in the binomial

How to recognize that it is a Binomial Squared:

1) Is it a trinomial? ( if it’s a binomial it cannot be a binomial squared)
2) Are the first  and last terms POSITIVE?
3) Are the first and last terms PERFECTSQUARES?
4) Is the middle term DOUBLE the product of the SQRTS of the 1^st and last terms?

If YES to ALL of these questions you have a trinomial square

To FACTOR a Trinomial Square
a² + 6a + 9 (called a trinomial square)

1) Put ONE set of {{HUGS} with an exponent of 2  (  )²
2) Put the sign of the middle term inside  (in this case its +)  (  +  )²
3) Find the SQRT’s of the first term & last terms; place them in parentheses (a +3)²
4) Check by FOILing back

If the sign is negative in the middle, simple use a negative sign when you factor.