Hey, I need help factoring x^4 - 26x^2 + 25?

Question

Hey, I need help factoring x^4 - 26x^2 + 25. Please show work and explain. THANKS

Answer 1

x^4 - 26x^2 + 25 = (x^2 - 25)(x^2 - 1) = (x - 5)(x + 5)(x - 1)(x + 1)

Answer 2

X^4 - 26 X^2 + 25 = ( X^2 - 25 ) ( X^2 -1 )

Answer 3

Let y = x^2

So, x^4 -26x^2 + 25

would be the same as

y^2 - 26 y + 25

=> y^2 - 25y -y + 25
=> y(y-25) - 1 (y-25)
=> (y - 1)(y-25)

So, if the equation was

(y - 1)(y-25) = 0

Then
y = 1
or
y = 25

So,
x^2 = 1
=> x = +1 or -1

OR

x^2 = 25
=> x = +5 or -5

So, x can have values +1 / -1 / +5 / -5

Answer 4

When I get big powers, I like to simplify it a little and choose a new variable.

a = x^2, so a^2 = x^4

x^4 - 26x^2 + 25
a^2 - 26a + 25

Find two #s that multiply to 25 and add to - 26 = -1 and - 25

(a - 1)(a - 25)

Now just substitute your x^2 back in:

(x^2 -1)(x^2 - 25)

Answer 5

Just factor it using simple trinomial factoring follwed by difference of squares:

(x^2 - 25)(x^2 - 1) <--- multiply to 25 and add to -26
=(x - 5)(x+5)(x-1)(x+1)

There can't be roots since it isnt an equation just an expression!

Answer 6

are you sure about that formula?