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The trinomial $1+a^{10}-2a^5$ is a perfect square trinomial, because it's discriminant is equal to zero
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$\Delta=b^2-4ac=-2^2-4\left(1\right)\left(1\right) = 0$
Learn how to solve polynomial factorization problems step by step online. Factor the expression 1+a^10-2a^5. The trinomial 1+a^{10}-2a^5 is a perfect square trinomial, because it's discriminant is equal to zero. Using the perfect square trinomial formula. Factoring the perfect square trinomial. We can factor the polynomial \left(a^{5}-1\right) using the rational root theorem, which guarantees that for a polynomial of the form a_nx^n+a_{n-1}x^{n-1}+\dots+a_0 there is a rational root of the form \pm\frac{p}{q}, where p belongs to the divisors of the constant term a_0, and q belongs to the divisors of the leading coefficient a_n. List all divisors p of the constant term a_0, which equals -1.