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# Factor the expression $1+a^{10}-2a^5$

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##  Final answer to the problem

$\left(a^{4}+a^{3}+a^{2}+a+1\right)^{2}\left(a-1\right)^{2}$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Integrate by partial fractions
• Product of Binomials with Common Term
• FOIL Method
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Prove from LHS (left-hand side)
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1

The trinomial $1+a^{10}-2a^5$ is a perfect square trinomial, because it's discriminant is equal to zero

$\Delta=b^2-4ac=-2^2-4\left(1\right)\left(1\right) = 0$

Learn how to solve polynomial factorization problems step by step online.

$\Delta=b^2-4ac=-2^2-4\left(1\right)\left(1\right) = 0$

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.

##  Final answer to the problem

$\left(a^{4}+a^{3}+a^{2}+a+1\right)^{2}\left(a-1\right)^{2}$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

###  Main Topic: Polynomial Factorization

They are a group of techniques that help us rewrite polynomial expressions as a product of factors.