Question

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

Answer 1

Answer:

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

Step-by-step explanation:

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

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

STEP 2: Let $u=x^{2}$. Substitute $u$ 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 $u$ with $x^2$.

$(x^{2} -4)(x^{2} -1)$

STEP 5: Rewrite $4$ 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 $1$ as $1^{2}$.

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

STEP 8: Factor.

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