SME
Grade 9 Math · Algebra 1
Factoring polynomials: GCF, trinomials and special products
Use this for “Factor x² + 2x − 15.”
Diagram
The tiles of x² + 2x − 15 make a rectangle (x + 5) by (x − 3): (x + 5)(x − 3) = x² + 2x − 15.
3 positive and negative x tiles cancel as zero pairs.
This is an example. Type your own values to start a new problem.
x²
+
b
x
+
(
c
)
=
(x
+
p
)(x
+
(
q
)
)
Formulas
p
=
the
number
in
the
pair
of
c
that
adds
to
b
5 = the number in the pair of −15 that adds to 2
q
=
b
−
p
−3 = 2 − 5
Assumptions
•
Find two numbers whose product is c and whose sum is b.
•
Check by multiplying the brackets back out.
•
Not every trinomial factors over the integers.
Step-by-step
WE KNOW
b = 2, c = −15
FIND
first number (p), second number (q)
Step 1 · Find first number (p)
Use p = the number in the pair of c that adds to b
List
the
factor
pairs
of
c
and
find
the
pair
that
adds
to
b
;
p
is
the
larger
of
the
two.
p
=
the
number
in
the
pair
of
−15
that
adds
to
2
5 × (−3) = −15
5 − 3 = 2
p
=
5
Step 2 · Find second number (q)
Use q = b − p
The
two
numbers
add
to
b
.
q
=
2
−
5
q
=
−3
→
x
2
+
2x
−
15
=
(x
+
5)(x
−
3)
Check
Put the numbers back in. Both sides should match.
5 × (−3) = −15 ✓
5 + (−3) = 2 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.