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5. Solve (x + 1)(x + 2)(x + 3)(x + 4) = 120.
Answers
Answered by
1
Step-by-step explanation:
Multiplying out we have:
(
x
+
1
)
(
x
+
2
)
(
x
+
3
)
(
x
+
4
)
−
120
=
x
4
+
10
x
3
+
35
x
2
+
50
x
−
96
Can you find a pair of rational (actually, integer) zeroes of this polynomial? Hint:
120
=
2
×
3
×
4
×
5
=
(
−
5
)
×
(
−
4
)
×
(
−
3
)
×
(
−
2
)
When you get these roots, they become the values of
a
and
b
in the above answer. Beware that one of these is negative. Divide by those two factors
x
−
a
,
x
−
b
and you are left with a quadratic quotient
x
2
+
c
x
+
d
that has no more real roots (because the discriminant
c
2
−
4
d
is negative).
Factoring is as much an art as a science.
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