Question

ve
5. Solve (x + 1)(x + 2)(x + 3)(x + 4) = 120.​

Answer 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.