Identify a value k that makes (x+5) a factor of x^3+kx^2-x+45
will mark brainliest
1 answer:
Answer:
We should attempt synthetic division to find when
x
3
−
k
x
2
+
2
k
x
−
15
x
−
3
has a remainder of
0
, which would signify that it is a factor of the polynomial.
The synthetic substitution would be set up as:
3
−
∣
∣
∣
1
−
k
2
k
−
15
−−−
−−−
−−−
−−−
−−−
|
0
Treating the synthetic division like any other synthetic division problem, we see that
3
−
∣
∣
∣
1
−
k
2
k
−
15
−−−
−−−
3
−−−−−−−−
−
3
k
+
9
−−−−−−−−
−
3
k
+
27
−−−−−−−−−
1
−
k
+
3
−
k
+
9
|
0
If the remainder equals
0
, then we know that
−
3
k
+
27
+
(
−
15
)
=
0
Solve this to see that
k
=
4
.
Thus,
(
x
−
3
)
is a factor of
x
3
−
4
x
2
+
8
x
−
15
.
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Answer:
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