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4 votes
Please help!!

I need to factor P(x)=x^4+50x^2+625
I thought the answer was P(x)=(x^2+25)^2
But it isn’t could someone please help with the answer?

User Erichui
by
8.7k points

1 Answer

1 vote

x

4

+

50

x

2

+

625Rewrite

625

as

25

2

.

u

2

+

50

u

+

25

2

Check the middle term by multiplying

2

a

b

and compare this result with the middle term in the original expression.

2

a

b

=

2

u

25

Simplify.

2

a

b

=

50

u

Factor using the perfect square trinomial rule

a

2

+

2

a

b

+

b

2

=

(

a

+

b

)

2

, where

a

=

u

and

b

=

25

.

(

u

+

25

)

2

Replace all occurrences of

u

with

x

2

.

(

x

2

+

25

)

2

User Alex Kovanev
by
8.3k points

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