Factor x^4-5x^2+4 show your work

Question

asked Jun 18, 2021 145k views

1 Answer

Matias Andina · Answer 1 · 2021-06-24T22:14:43+0000

Answer:

(x+2)(x-2)(x+1)(x-1)

Explanation:

STEP 1: Rewrite
x^(4) as
(x^2)^2 .

(x^2)^2-5x^2+4

STEP 2: Let
u=x^(2) . Substitute
for all occurrences of
x^(2) .

u^2-5u+4

STEP 3: Factor
u^2-5u+4 using the AC method.

(u-4)(u-1)

STEP 4: Replace all occurrences of
with
x^2 .

(x^(2) -4)(x^(2) -1)

STEP 5: Rewrite
as
2^(2) .

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

STEP 6: Since both terms are perfect squares, factor using the difference of squares formula,
a^2-b^2=(a+b)(a-b) where
a=x and
b=2 .

(x+2)(x-2)(x^(2)-1)

STEP 7: Rewrite
as
1^(2) .

(x+2)(x-2)(x^2-1^2)

STEP 8: Factor.

(x+2)(x-2)(x+1)(x-1)