SME
Grade 9 Math · Problem type
Add and subtract polynomials
Use this for “(3x² − 2x + 5) − (x² + 4x − 1)”.
Diagram
(3x² − 2x + 5) + (−x² − 4x + 1) = 2x² − 6x + 6.
1 zero pair cancels: struck out.
This is an example. Type your own values to start a new problem.
(
a
x²
+
(
b
)
x
+
c
)
(
d
x²
+
e
x
+
(
f
)
)
=
p
x²
+
(
q
)
x
+
r
Formulas
p
=
a
±
d
,
−
when
o
is
−
2 = 3 ± 1, − when − is −
q
=
b
±
e
,
−
when
o
is
−
−6 = −2 ± 4, − when − is −
r
=
c
±
f
,
−
when
o
is
−
6 = 5 ± −1, − when − is −
Assumptions
•
Only like terms combine: x² with x², x with x, numbers with numbers.
•
To subtract, add the opposite: change the sign of every term in the second bracket.
•
A positive and a negative tile of the same size make zero.
Step-by-step
WE KNOW
a = 3, b = −2, c = 5, o: −, d = 1, e = 4, f = −1
FIND
x² in the answer (p), x in the answer (q), number in the answer (r)
Step 1 · Find x² in the answer (p)
Use p = a ± d, − when o is −
Subtracting
adds
the
opposite:
−(
x
2
+
4x
−
1)
=
−
x
2
−
4x
+
1.
Combine
the
x
2
terms,
the
second
one’s
sign
changed.
p
=
a
−
d
p
=
3
−
1
p
=
2
Step 2 · Find x in the answer (q)
Use q = b ± e, − when o is −
Subtracting adds the opposite: combine the x terms, the second one’s sign changed.
q
=
b
−
e
q
=
−2
−
4
q
=
−6
Step 3 · Find number in the answer (r)
Use r = c ± f, − when o is −
Subtracting adds the opposite: combine the numbers, the second one’s sign changed.
r
=
c
−
f
r
=
5
−
(−1)
r
=
6
→
2x²
−
6x
+
6
Check
Put the numbers back in. Both sides should match.
2 = 3 − 1 ✓
−6 = −2 − 4 ✓
6 = 5 − (−1) ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.