What is factor 1+a^{10}-2a^5 ?

The solution to factor 1+a^{10}-2a^5 is (a-1)^2(a^4+a^3+a^2+a+1)^2

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factor 1+a^{10}-2a^5

factor

1 + a^{10} - 2 a^{5}

(a - 1)^{2} (a^{4} + a^{3} + a^{2} + a + 1)^{2}

Solution steps

1 + a^{10} - 2 a^{5}

Write in the standard form

= a^{10} - 2 a^{5} + 1

Use the rational root theorem

= (a - 1) \frac{a ^{10} - 2 a ^{5} + 1}{a - 1}

\frac{a ^{10} - 2 a ^{5} + 1}{a - 1} = a^{9} + a^{8} + a^{7} + a^{6} + a^{5} - a^{4} - a^{3} - a^{2} - a - 1

= (a - 1) (a^{9} + a^{8} + a^{7} + a^{6} + a^{5} - a^{4} - a^{3} - a^{2} - a - 1)

Factor

a^{9} + a^{8} + a^{7} + a^{6} + a^{5} - a^{4} - a^{3} - a^{2} - a - 1 : (a^{4} + a^{3} + a^{2} + a + 1) (a - 1) (a^{4} + a^{3} + a^{2} + a + 1)

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

Simplify

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

6 x - \frac{2 x + 3}{5} = \frac{x - 5}{4} - x

5 x = - 25

\frac{2}{3} x - 12 = x

7 x - 9 - 11 = 3 x + 4 + 2 x

w^{2} = 36

What is factor 1+a^{10}-2a^5 ?
The solution to factor 1+a^{10}-2a^5 is (a-1)^2(a^4+a^3+a^2+a+1)^2