What is factor (x-3)^4+2(x-3)^2-8 ?

The solution to factor (x-3)^4+2(x-3)^2-8 is (x^2-6x+7)(x^2-6x+13)

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factor (x-3)^4+2(x-3)^2-8

factor

(x - 3)^{4} + 2 (x - 3)^{2} - 8

(x^{2} - 6 x + 7) (x^{2} - 6 x + 13)

Solution steps

(x - 3)^{4} + 2 (x - 3)^{2} - 8

Let

u = (x - 3)^{2}

= u^{2} + 2 u - 8

Factor

u^{2} + 2 u - 8 : (u - 2) (u + 4)

= (u - 2) (u + 4)

Substitute back

u = (x - 3)^{2}

= ((x - 3)^{2} - 2) ((x - 3)^{2} + 4)

Expand

(x - 3)^{2} - 2 : x^{2} - 6 x + 7

= (x^{2} - 6 x + 7) ((x - 3)^{2} + 4)

Expand

(x - 3)^{2} + 4 : x^{2} - 6 x + 13

= (x^{2} - 6 x + 7) (x^{2} - 6 x + 13)

e^{2 x} + 3 e^{x} + 2

- 9 108 + 63

1 - 3 a^{2} + 3 a^{4} - a^{6}

64 - 8 1^{2}

2 a x - b x + 2 a y - b y

What is factor (x-3)^4+2(x-3)^2-8 ?
The solution to factor (x-3)^4+2(x-3)^2-8 is (x^2-6x+7)(x^2-6x+13)