Write as a Set of Linear Factors x^4-4x^3+13x^2-36x+36

$x^{4} - 4 x^{3} + 13 x^{2} - 36 x + 36$

Regroup terms.

$- 4 x^{3} - 36 x + x^{4} + 13 x^{2} + 36$

Factor $- 4 x$ out of $- 4 x^{3} - 36 x$ .

Factor $- 4 x$ out of $- 4 x^{3}$ .

$- 4 x (x^{2}) - 36 x + x^{4} + 13 x^{2} + 36$

Factor $- 4 x$ out of $- 36 x$ .

$- 4 x (x^{2}) - 4 x (9) + x^{4} + 13 x^{2} + 36$

Factor $- 4 x$ out of $- 4 x (x^{2}) - 4 x (9)$ .

$- 4 x (x^{2} + 9) + x^{4} + 13 x^{2} + 36$

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

$- 4 x (x^{2} + 9) + {(x^{2})}^{2} + 13 x^{2} + 36$

Let $u = x^{2}$ . Substitute $u$ for all occurrences of $x^{2}$ .

$- 4 x (x^{2} + 9) + u^{2} + 13 u + 36$

Factor $u^{2} + 13 u + 36$ using the AC method.

Consider the form $x^{2} + i x + c$ . Find a pair of integers whose product is $c$ and whose sum is $i$ . In this case, whose product is $36$ and whose sum is $13$ .

$4, 9$

Write the factored form using these integers.

$- 4 x (x^{2} + 9) + (u + 4) (u + 9)$

Replace all occurrences of $u$ with $x^{2}$ .

$- 4 x (x^{2} + 9) + (x^{2} + 4) (x^{2} + 9)$

Factor $x^{2} + 9$ out of $- 4 x (x^{2} + 9) + (x^{2} + 4) (x^{2} + 9)$ .

Factor $x^{2} + 9$ out of $- 4 x (x^{2} + 9)$ .

$(x^{2} + 9) (- 4 x) + (x^{2} + 4) (x^{2} + 9)$

Factor $x^{2} + 9$ out of $(x^{2} + 4) (x^{2} + 9)$ .

$(x^{2} + 9) (- 4 x) + (x^{2} + 9) (x^{2} + 4)$

Factor $x^{2} + 9$ out of $(x^{2} + 9) (- 4 x) + (x^{2} + 9) (x^{2} + 4)$ .

$(x^{2} + 9) (- 4 x + x^{2} + 4)$

Let $u = x$ . Substitute $u$ for all occurrences of $x$ .

$(x^{2} + 9) (- 4 u + u^{2} + 4)$

Factor using the perfect square rule.

Rearrange terms.

$(x^{2} + 9) (u^{2} - 4 u + 4)$

Rewrite $4$ as $2^{2}$ .

$(x^{2} + 9) (u^{2} - 4 u + 2^{2})$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$4 u = 2 \cdot u \cdot 2$

Rewrite the polynomial.

$(x^{2} + 9) (u^{2} - 2 \cdot u \cdot 2 + 2^{2})$

Factor using the perfect square trinomial rule $a^{2} - 2 a i + i^{2} = {(a - i)}^{2}$ , where $a = u$ and $i = 2$ .

$(x^{2} + 9) {(u - 2)}^{2}$

Replace all occurrences of $u$ with $x$ .

$(x^{2} + 9) {(x - 2)}^{2}$

Write as a Set of Linear Factors x^4-4x^3+13x^2-36x+36

Related Questions

Support LCMGCF.com by disabling your adblocker.