Question

Factor each completely. x^8- 10x^4 + 9 = 0 ?

Answer 1

Is this what you wanted?

Step-by-step explanation:

First, say that

x

4

=

u

.

The equation then can be written as

u

2

−

10

u

+

9

=

0

This more likely looks familiar.

This can be factored into

(

u

−

9

)

(

u

−

1

)

=

0

From here it can be said that if the product of two terms is

0

, at least one of the terms must be equal to

0

, so set both terms equal to

0

to find when this is true.

u

−

9

=

0

u

−

1

=

0

Which can be rewritten as

u

=

9

u

=

1

Now, go back to the beginning when we said that

x

4

=

u

. Replace each instance of

u

with

x

4

.

x

4

=

9

x

4

=

1

Solve each.

x

4

=

3

2

x

=

±

(

3

2

)

1

4

x

=

±

(

3

)

1

2

x

=

±

√

3

x

4

=

1

x

=

±

1

When in doubt, check a graph:

graph{x^8-10x^4+9 [-13.64, 14.84, -2.16, 12.08]}

The zeros (solutions) are at

x

=

±

1

,

±

√

3

.