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# Factor the expression $5x^4-2x^2-3$

## Step-by-step Solution

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###  Videos

$\left(5x^{2}+3\right)\left(x+1\right)\left(x-1\right)$
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##  Step-by-step Solution 

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We can factor the polynomial $5x^4-2x^2-3$ 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 $-3$

$1, 3$

Learn how to solve factorization problems step by step online.

$1, 3$

Learn how to solve factorization problems step by step online. Factor the expression 5x^4-2x^2+-3. We can factor the polynomial 5x^4-2x^2-3 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 -3. Next, list all divisors of the leading coefficient a_n, which equals 5. The possible roots \pm\frac{p}{q} of the polynomial 5x^4-2x^2-3 will then be. Trying all possible roots, we found that 1 is a root of the polynomial. When we evaluate it in the polynomial, it gives us 0 as a result.

$\left(5x^{2}+3\right)\left(x+1\right)\left(x-1\right)$

##  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

SimplifyFactorFactor by completing the squareFind the integralFind the derivativeFind 5x^4+-2x^2 using the definitionFind the rootsFind break even pointsFind the discriminant

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0
a
b
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n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
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: Factorization

In mathematics, factorization or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original.

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