Work out
(x + 3) × (___________) = x^2 − 2x − 15
Answers
Answer:
Step-by-step explanation:
Answer 2 of 2
x
−
5
Have a look at the method. It shows a useful 'trick'.
Explanation:
Given:
x
2
−
2
x
−
15
x
+
3
...
...
...
...
...
...
...
...
(
1
)
Not all questions permit this approach of solution!
Consider
.
.
x
2
−
2
x
−
15
This can be factored into:
(
x
−
5
)
(
x
+
3
)
...
...
...
...
...
...
...
...
...
.
.
(
2
)
Substitute expression (2) into expression (1)
(
x
−
5
)
(
x
+
3
)
x
+
3
Write as:
x
+
3
x
+
3
×
(
x
−
5
)
But
x
+
3
x
+
3
has the value of 1 giving
1
×
(
x
−
5
)
x
−
5
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Foot note
Consider:
x
+
3
x
+
3
If you were investigating values then this produces a problem.
You are not mathematically allowed to divide by 0.
So
x
+
3
x
+
3
is 'Undefined' at
x
=
−
3
For this very reason
0
0
does
not equal 1
−−−−−−−−−−
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Answer link
Tony B
Jun 21, 2018
Answer 1 of 2
Using polynomial long division.
x
−
5
Explanation:
Given:
(
x
2
−
2
x
−
15
)
÷
(
x
+
3
)
ddddddd.dd
x
2
−
2
x
−
15
x
(
x
+
3
)
→
x
2
+
3
x
←
Subtract
−−−−−−−−−−−−−−−−−−−
dddddddddd
0
,
−
5
x
−
15
−
5
(
x
+
3
)
→
d
−
5
x
−
15
←
Subtract
−−−−−−−−−−−−−−−−−−−−−
dddddddddddddd
0
+
0
(
x
2
−
2
x
−
15
)
÷
(
x
+
3
)
=
x
−
5