What is factor x^4-4x^3+8x^2-16x+16 ?

The solution to factor x^4-4x^3+8x^2-16x+16 is (x-2)^2(x^2+4)

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factor x^4-4x^3+8x^2-16x+16

factor

x^{4} - 4 x^{3} + 8 x^{2} - 16 x + 16

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

Solution steps

x^{4} - 4 x^{3} + 8 x^{2} - 16 x + 16

Use the rational root theorem

= (x - 2) \frac{x ^{4} - 4 x ^{3} + 8 x ^{2} - 16 x + 16}{x - 2}

\frac{x ^{4} - 4 x ^{3} + 8 x ^{2} - 16 x + 16}{x - 2} = x^{3} - 2 x^{2} + 4 x - 8

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

Factor

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

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

Apply exponent rule:

aa = a^{2}

(x - 2) (x - 2) = (x - 2)^{2}

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

\frac{3}{4} (x + 8) > \frac{1}{2} (2 x + 10)

\frac{1}{2} + \frac{x}{2} < \frac{1}{3} + \frac{x}{3}

8 x - 27 - 10 - 6 x = 15

7 = x - 4

∣ 6 - d ∣ + 4 = 3 d + 18

What is factor x^4-4x^3+8x^2-16x+16 ?
The solution to factor x^4-4x^3+8x^2-16x+16 is (x-2)^2(x^2+4)