Checklist of Types of factoring we will practice
Simple Factoring: factoring out a common factor
eg. 5x ‐15 = 5(x ‐3)
Factoring of Quadratic Trinomials: ax2 +bx +c
1) Monic, where a = 1 ex. x2 + 3x + 2 = (x+1) (x+2) ("tri" means 3)
2) Complex, where a ≠ 0,1 ex. 4x2 + 4x ­ 3 = (2x ­1)(2x+3)
3) Differences of Squares, where b = 0 ex. x2 ­ 25 = (x+5)(x­5)
Completing the square
Puts expressions into vertex form: y = a(x‐h)2+k
Factoring Complex Trinomials.
Write an equation for the area represented below.
x
2
x
2
1
When a≠0,1 in y = ax2+bx+c, the trinomial is called a COMPLEX TRINOMIAL.
Complex trinomials can be factored using a variety of methods. We will explore some methods:
1. algebra tiles
2. "fill in the box" method 3. decomposition
4. the real SPI
Complex Trinomial Factoring method: fill in the box
5x2+12x+4
1) Use the quadratic as an expression for area.
Fill in the a and c terms within the box. We do not know how
b will be split up yet, so leave it alone.
2) Determine the possible values that would give a and c.
3) Check which ones would also give you b.
2
Complex Trinomial Factoring method: decomposition
5x2+12x+4
S=
P=
I =
1) Determine the integers that work for S and P.
2) Break up the x‐term into the integers you found in step 1.
3) Simple factor the 1st two terms, and simple factor the remaining two terms.
They do not have the be the same GCF. If this is done properly, we should get
two brackets that are identical.
4) common factor again ("Leftovers go in one bracket"). TADA!
Complex Trinomial Factoring method: the REAL SPI
In general, for ax2+bx+c: S is b and
P is the product of a and c
5x2+12x+4
S=
P=
I =
1) Determine the integers that work for S and P.
2) Divide both values by a.
3) Remaining fractions (g/f, j/h) gives you the coefficients of your factors: (fx+g)(hx+j)
‐numerator is for g and j
‐denominator is for f and h
3
Factor the following expressions:
(answers at bottom)
2
a) 6x +11x+5
b) 2x2 +3x ­ 5
c) x2+10x + 25
d) 14x2­19x­3
ing
and
p
x
e
y b
r
e
sw
an
our
y
k
hec
C
a) b)
c)
d)
HW: p. 307 # 5*, 6*, 7*.
*Do at least 5 from each question
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