Factor x^2-14x+49+4x^9-28x^8

$x^{2} - 14 x + 49 + 4 x^{9} - 28 x^{8}$

Step 1

Regroup terms.

$4 x^{9} - 28 x^{8} + x^{2} - 14 x + 49$

Step 2

Factor $4 x^{8}$ out of $4 x^{9} - 28 x^{8}$ .

Factor $4 x^{8}$ out of $4 x^{9}$ .

$4 x^{8} (x) - 28 x^{8} + x^{2} - 14 x + 49$

Factor $4 x^{8}$ out of $- 28 x^{8}$ .

$4 x^{8} (x) + 4 x^{8} (- 7) + x^{2} - 14 x + 49$

Factor $4 x^{8}$ out of $4 x^{8} (x) + 4 x^{8} (- 7)$ .

$4 x^{8} (x - 7) + x^{2} - 14 x + 49$

Step 3

Factor using the perfect square rule.

Rewrite $49$ as $7^{2}$ .

$4 x^{8} (x - 7) + x^{2} - 14 x + 7^{2}$

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

$14 x = 2 \cdot x \cdot 7$

Rewrite the polynomial.

$4 x^{8} (x - 7) + x^{2} - 2 \cdot x \cdot 7 + 7^{2}$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 7$ .

$4 x^{8} (x - 7) + {(x - 7)}^{2}$

Step 4

Factor $x - 7$ out of $4 x^{8} (x - 7) + {(x - 7)}^{2}$ .

Factor $x - 7$ out of $4 x^{8} (x - 7)$ .

$(x - 7) (4 x^{8}) + {(x - 7)}^{2}$

Factor $x - 7$ out of ${(x - 7)}^{2}$ .

$(x - 7) (4 x^{8}) + (x - 7) (x - 7)$

Factor $x - 7$ out of $(x - 7) (4 x^{8}) + (x - 7) (x - 7)$ .

$(x - 7) (4 x^{8} + x - 7)$