SME
Grade 9 Math · Problem type
Take out the greatest common factor
Use this for “Factor 6x² + 15x.”
Diagram
The tiles of 6x² + 15x make a rectangle 3x by (2x + 5): 3x(2x + 5) = 6x² + 15x.
This is an example. Type your own values to start a new problem.
a
x²
+
b
x
=
g
x(
p
x
+
q
)
Formulas
g
=
greatest
common
factor
of
a
and
b
3 = greatest common factor of 6 and 15
p
=
a
g
2
=
6
3
q
=
b
g
5
=
15
3
Assumptions
•
Find the greatest common factor of the coefficients; x divides both terms too.
•
Divide each term by the common factor to fill the bracket.
•
Check by distributing back.
Step-by-step
WE KNOW
a = 6, b = 15
FIND
greatest common factor (g), x in the bracket (p), number in the bracket (q)
Step 1 · Find greatest common factor (g)
Use g = greatest common factor of a and b
The largest whole number that divides both coefficients.
g
=
greatest
common
factor
of
6
and
15
g
=
3
Step 2 · Find x in the bracket (p)
Use p = a ÷ g
Divide
the
x
2
term
by
gx:
what
is
left
is
px.
p
=
6
3
p
=
2
Step 3 · Find number in the bracket (q)
Use q = b ÷ g
Divide the x term by gx: what is left is a number.
q
=
15
3
q
=
5
→
6x²
+
15x
=
3x(2x
+
5)
Check
Put the numbers back in. Both sides should match.
3 = greatest common factor of 6 and 15 ✓
2
=
6
3
✓
5
=
15
3
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.