What is factor k^4-4k^2+8k^3-32k+12k^2-48 ?

The solution to factor k^4-4k^2+8k^3-32k+12k^2-48 is (k-2)(k+2)^2(k+6)

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factor k^4-4k^2+8k^3-32k+12k^2-48

factor

k^{4} - 4 k^{2} + 8 k^{3} - 32 k + 12 k^{2} - 48

(k - 2) (k + 2)^{2} (k + 6)

Solution steps

k^{4} - 4 k^{2} + 8 k^{3} - 32 k + 12 k^{2} - 48

Add similar elements:

- 4 k^{2} + 12 k^{2} = 8 k^{2}

= k^{4} + 8 k^{2} + 8 k^{3} - 32 k - 48

Write in the standard form

= k^{4} + 8 k^{3} + 8 k^{2} - 32 k - 48

Use the rational root theorem

= (k - 2) \frac{k ^{4} + 8 k ^{3} + 8 k ^{2} - 32 k - 48}{k - 2}

\frac{k ^{4} + 8 k ^{3} + 8 k ^{2} - 32 k - 48}{k - 2} = k^{3} + 10 k^{2} + 28 k + 24

= (k - 2) (k^{3} + 10 k^{2} + 28 k + 24)

Factor

k^{3} + 10 k^{2} + 28 k + 24 : (k + 2) (k + 2) (k + 6)

= (k - 2) (k + 2) (k + 2) (k + 6)

Apply exponent rule:

aa = a^{2}

(k + 2) (k + 2) = (k + 2)^{2}

= (k - 2) (k + 2)^{2} (k + 6)

28 (10 - \frac{28}{3.5}) = x

1027

3 x + 7 = - 8

(z y x)^{8}

(x + 7)^{2} + 1 = 12

What is factor k^4-4k^2+8k^3-32k+12k^2-48 ?
The solution to factor k^4-4k^2+8k^3-32k+12k^2-48 is (k-2)(k+2)^2(k+6)