A.SSE.3a: Factor Quadratic Expressions
A.SSE.3a: Factor Quadratic Expressions
Write expressions in equivalent forms to solve problems.
3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the
expression.?3?
a. Factor a quadratic expression to reveal the zeros of the function it defines.
Overview of Lesson
- activate prior knowledge
- present vocabulary and/or big ideas associated with the lesson
- connect assessment practices with curriculum
- model an assessment problem and solution strategy
- facilitate guided practice of student activity
Optional: Provide or allow students to create additional problem sets
- facilitate a summary and share out of student work
Optional HW - Write the math assignment.
Factoring by Grouping (This method works with any factorable trinomial).
1. Start with a factorable trinomial:
7. Replace the middle term of the
2
trinomial with two new terms.
8x  22 x  15
8x 2  8x  15x  15
b 2  4ac  222  4  8 15 
8. Group the new polynomial into two
b 2  4ac  4
binomials using parentheses..
2
8 x 2  8 x  15 x  15
b  4ac  2


2. Identify the values of a, b, and c
a=8
b=22
c=15
3. Multiply a times c.
ac  120
ac=120
9. Factor each binomial. (Note that the
factors in parenthesis will always be
identical.)
8 x 2  8 x  15 x  15
4. Find the factors of ac
10.Extract the common factor and add the
remaining terms as a second factor.
1
2
3
4
5
120
60
40
30
24


8 x  x  1  15  x  1
6 20
8 15
10 12
12 10
5. Box the set of factors in step 4 whose
sum or difference equals b
 x  1
 x  18 x  15
6. Assign a positive or negative value to
each factor. Write the signed factors
below.
+
8
+
15
=
11. Check. Use the distributive property
of multiplication to make sure that
your binomials in Step 10 return you
to the trinomial that you started with
in Step 1. If so, put a check mark
here.
 x  1 8 x  15
22
b
8 x 2  15 x  8 x  15
8 x 2  22 x  15
REGENTS PROBLEMS
1. Keith determines the zeros of the function
a.
b.
to be
c.
d.
2. Which equation has the same solutions as
a.
b.
c.
d.
3. In the equation
4. Solve
and 5. What could be Keith's function?
, b is an integer. Find algebraically all possible values of b.
for m by factoring.
A.SSE.3a: Factor Quadratic Expressions
Answer Section
1. ANS: C
Strategy: Convert the zeros to factors.
If the zeros of
are
and 5, then the factors of
Therefore, the function can be written as
The correct answer choice is c.
PTS: 2
REF: 061412a1
2. ANS: D
Strategy 1: Factor by grouping.
are
NAT: A.SSE.3a
and
.
.
TOP: Solving Quadratics
Answer choice d is correct
Strategy 2: Work backwards by using the disrtibutive property to expand all answer choices and match the
expanded trinomials to the function
.
a.
c.
b.
PTS: 2
3. ANS:
REF: 011503a1
d.
NAT: A.SSE.3a
TOP: Solving Quadratics
6 and 4
Strategy: Factor the trinomial
into two binomials.
Possible values for a and c are 4 and 6.
PTS: 2
4. ANS:
REF: 081425a1
NAT: A.SSE.3a
and
Strategy: Factor by grouping.
Use the multiplication property of zero to solve for m.
TOP: Solving Quadratics
PTS: 2
REF: fall1305a1
NAT: A.SSE.3a
TOP: Solving Quadratics