(x⁴ – 10x² + 24x) ÷ (x + 4)
division of polynomials
Answers
Answered by
0
Step-by-step explanation:
Given:
f
(
x
)
=
x
4
−
10
x
2
+
24
Note that this quartic contains only terms of even degree, so we can start to factor it as a quadratic in
x
2
.
Note also that
10
=
4
+
6
and
24
=
4
⋅
6
Hence we find:
x
4
−
10
x
2
+
24
=
(
x
2
−
4
)
(
x
2
−
6
)
x
4
−
10
x
2
+
24
=
(
x
2
−
2
2
)
(
x
2
−
(
√
6
)
2
)
x
4
−
10
x
2
+
24
=
(
x
−
2
)
(
x
+
2
)
(
x
−
√
6
)
(
x
+
√
6
)
Hence zeros:
x=±2 and x=±√6
graph{x^4-10x^2+24 [-5.067, 4.933, -6, 32]}
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Answered by
10
Step-by-step explanation:
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