What is factor (x-6)^{7/2}-36(x-6)^{3/2} ?

The solution to factor (x-6)^{7/2}-36(x-6)^{3/2} is x(x-12)(x-6)^{3/2}

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factor (x-6)^{7/2}-36(x-6)^{3/2}

factor

(x - 6)^{\frac{7}{2}} - 36 (x - 6)^{\frac{3}{2}}

x (x - 12) (x - 6)^{\frac{3}{2}}

Solution steps

(x - 6)^{\frac{7}{2}} - 36 (x - 6)^{\frac{3}{2}}

Rewrite

(x - 6)^{\frac{7}{2}}

(x - 6)^{7}

= (x - 6)^{7} - 36 (x - 6)^{\frac{3}{2}}

Rewrite

(x - 6)^{\frac{3}{2}}

(x - 6)^{3}

= (x - 6)^{7} - 36 (x - 6)^{3}

Factor out common term

(x - 6)^{3} : (x - 6)^{3} ((x - 6)^{4} - 36)

= (x - 6)^{3} ((x - 6)^{4} - 36)

Factor

(x - 6)^{4} - 36 : ((x - 6)^{2} + 6) ((x - 6)^{2} - 6)

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

Simplify

(x - 6)^{3} ((x - 6)^{2} + 6) ((x - 6)^{2} - 6) : x (x - 6)^{3} (x - 12)

= x (x - 6)^{3} (x - 12)

(x - 6)^{3} = (x - 6)^{\frac{3}{2}}

= x (x - 12) (x - 6)^{\frac{3}{2}}

40 x^{2} - 39 x - 40

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∣ x ∣ \leq 15

\frac{( ( 2 x + 1 ) ( 3 - x ) )}{( x ^{2} + 6 x + 8 ) ( x ^{2} + 1 )} \leq 0

k^{4} + k^{3} - k^{2}

What is factor (x-6)^{7/2}-36(x-6)^{3/2} ?
The solution to factor (x-6)^{7/2}-36(x-6)^{3/2} is x(x-12)(x-6)^{3/2}