What is factor 8cos^3(x)-4cos(x)+1 ?

The solution to factor 8cos^3(x)-4cos(x)+1 is (2cos(x)-1)(4cos^2(x)+2cos(x)-1)

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factor 8cos^3(x)-4cos(x)+1

factor

8 cos^{3} (x) - 4 cos (x) + 1

(2 cos (x) - 1) (4 cos^{2} (x) + 2 cos (x) - 1)

Solution steps

8 cos^{3} (x) - 4 cos (x) + 1

Use the rational root theorem

a_{0} = 1, a_{n} = 8

The dividers of

a_{0} : 1,

The dividers of

a_{n} : 1, 2, 4, 8

Therefore, check the following rational numbers:

\pm \frac{1}{1 , 2 , 4 , 8}

\frac{1}{2}

is a root of the expression, so factor out

2 cos (x) - 1

= (2 cos (x) - 1) \frac{8 cos ^{3} ( x ) - 4 cos ( x ) + 1}{2 cos ( x ) - 1}

\frac{8 cos ^{3} ( x ) - 4 cos ( x ) + 1}{2 cos ( x ) - 1} = 4 cos^{2} (x) + 2 cos (x) - 1

= (2 cos (x) - 1) (4 cos^{2} (x) + 2 cos (x) - 1)

u \cdot v (x) e^{2 x}

\frac{x ^{2} - 9}{3 - x}

- 14 (a)^{2} + 7.7 (a) + 8

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

\frac{55}{170}

What is factor 8cos^3(x)-4cos(x)+1 ?
The solution to factor 8cos^3(x)-4cos(x)+1 is (2cos(x)-1)(4cos^2(x)+2cos(x)-1)