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Factor the expression $\left(12\cos\left(3x\right)+6\cos\left(3x\right)^2+\cos\left(3x\right)^3\right)^2$

Step-by-step Solution

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Final Answer

$\cos\left(3x\right)^2\left(3+\left(\cos\left(3x\right)+3\right)^2\right)^2$
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Step-by-step Solution

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Factor the polynomial $\left(12\cos\left(3x\right)+6\cos\left(3x\right)^2+\cos\left(3x\right)^3\right)$ by it's greatest common factor (GCF): $\cos\left(3x\right)$

$\left(\cos\left(3x\right)\left(12+6\cos\left(3x\right)+\cos\left(3x\right)^2\right)\right)^2$

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$\left(\cos\left(3x\right)\left(12+6\cos\left(3x\right)+\cos\left(3x\right)^2\right)\right)^2$

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Learn how to solve factor problems step by step online. Factor the expression (12cos(3x)+6cos(3x)^2cos(3x)^3)^2. Factor the polynomial \left(12\cos\left(3x\right)+6\cos\left(3x\right)^2+\cos\left(3x\right)^3\right) by it's greatest common factor (GCF): \cos\left(3x\right). The power of a product is equal to the product of it's factors raised to the same power. Add and subtract \displaystyle\left(\frac{b}{2a}\right)^2. Factor the perfect square trinomial \cos\left(3x\right)^2+6\cos\left(3x\right)+9.

Final Answer

$\cos\left(3x\right)^2\left(3+\left(\cos\left(3x\right)+3\right)^2\right)^2$

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

SimplifyFactor by completing the squareFind the integralFind the derivativeFind (12cos3x+6cos3x^2)^2 using the definitionSolve by quadratic formula (general formula)Find break even pointsFind the discriminant

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Function Plot

Plotting: $\cos\left(3x\right)^2\left(3+\left(\cos\left(3x\right)+3\right)^2\right)^2$

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0
a
b
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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

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