What is factor q^5-q^4-q^3+q^2 ?

The solution to factor q^5-q^4-q^3+q^2 is q^2(q-1)^2(q+1)

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factor q^5-q^4-q^3+q^2

factor

q^{5} - q^{4} - q^{3} + q^{2}

q^{2} (q - 1)^{2} (q + 1)

Solution steps

q^{5} - q^{4} - q^{3} + q^{2}

Factor out common term

q^{2} : q^{2} (q^{3} - q^{2} - q + 1)

= q^{2} (q^{3} - q^{2} - q + 1)

Factor

q^{3} - q^{2} - q + 1 : (q - 1) (q + 1) (q - 1)

= q^{2} (q - 1) (q + 1) (q - 1)

Apply exponent rule:

aa = a^{2}

(q - 1) (q - 1) = (q - 1)^{2}

= q^{2} (q - 1)^{2} (q + 1)

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

4 f + 4 f + 4 g

(3 + 1)^{2}

- y^{2} (- 8 x^{2} - 6 x y - y^{2})

(\frac{1 + 3 i}{2})^{165}

What is factor q^5-q^4-q^3+q^2 ?
The solution to factor q^5-q^4-q^3+q^2 is q^2(q-1)^2(q+1)