What is factor-2q^4+2q^3+q^2-1 ?

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

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factor-2q^4+2q^3+q^2-1

factor

- 2 q^{4} + 2 q^{3} + q^{2} - 1

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

Solution steps

- 2 q^{4} + 2 q^{3} + q^{2} - 1

Factor out

- 1 : - (2 q^{4} - 2 q^{3} - q^{2} + 1)

= - (2 q^{4} - 2 q^{3} - q^{2} + 1)

Factor

2 q^{4} - 2 q^{3} - q^{2} + 1 : (q - 1) (q - 1) (2 q^{2} + 2 q + 1)

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

Apply exponent rule:

aa = a^{2}

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

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

a^{2} + 11 a + 30 = 0

\frac{2}{\frac{5}{3}}

x^{4} + 3 x^{3} + x^{2} + 4 x + 3

\frac{1}{2} + \frac{1}{2} - \frac{3}{8}

\frac{1}{9} x^{2} + \frac{1}{3} x - 2 = 0

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