What is factor 2x^5-16x^3+x^2+24x-2 ?

The solution to factor 2x^5-16x^3+x^2+24x-2 is (x^2-2)(2x(x^2-6)+1)

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factor 2x^5-16x^3+x^2+24x-2

factor

2 x^{5} - 16 x^{3} + x^{2} + 24 x - 2

(x^{2} - 2) (2 x (x^{2} - 6) + 1)

Solution steps

2 x^{5} - 16 x^{3} + x^{2} + 24 x - 2

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

x^{5} = x x^{4}, x^{3} = x x^{2}

= 2 x x^{4} - 16 x x^{2} + x^{2} + 24 x - 2

Rewrite as

= 2 x x^{4} - 8 \cdot 2 x x^{2} + x^{2} + 12 \cdot 2 x - 2

Factor out common term

2 x

= 2 x (x^{4} - 8 x^{2} + 12) + x^{2} - 2

Factor

x^{4} - 8 x^{2} + 12 : (x^{2} - 2) (x^{2} - 6)

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

Rewrite as

= 2 (x^{2} - 2) x (x^{2} - 6) + 1 \cdot (x^{2} - 2)

Factor out common term

(x^{2} - 2)

= (x^{2} - 2) (2 x (x^{2} - 6) + 1)

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

d x (\frac{d y}{d x})

1 6^{2} + 16 x + 4

(- 4 a^{2} c) - 3 a c

\frac{5}{8} - 5 1^{3} m^{6}

What is factor 2x^5-16x^3+x^2+24x-2 ?
The solution to factor 2x^5-16x^3+x^2+24x-2 is (x^2-2)(2x(x^2-6)+1)