What is factor 2e^{3x}+4e^{2x}+e^x+2 ?

The solution to factor 2e^{3x}+4e^{2x}+e^x+2 is (e^x+2)(2e^{2x}+1)

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factor 2e^{3x}+4e^{2x}+e^x+2

factor

2 e^{3 x} + 4 e^{2 x} + e^{x} + 2

(e^{x} + 2) (2 e^{2 x} + 1)

Solution steps

2 e^{3 x} + 4 e^{2 x} + e^{x} + 2

Apply exponent rule:

a^{b c} = (a^{b})^{c}

e^{3 x} = (e^{x})^{3}, e^{2 x} = (e^{x})^{2}

= 2 (e^{x})^{3} + 4 (e^{x})^{2} + e^{x} + 2

= (2 (e^{x})^{3} + 4 (e^{x})^{2}) + (e^{x} + 2)

Factor out

2 (e^{x})^{2}

from

2 (e^{x})^{3} + 4 (e^{x})^{2} : 2 (e^{x})^{2} (e^{x} + 2)

= (e^{x} + 2) + 2 (e^{x})^{2} (e^{x} + 2)

Factor out common term

e^{x} + 2

= (e^{x} + 2) (2 (e^{x})^{2} + 1)

Simplify

(e^{x} + 2) (2 (e^{x})^{2} + 1) : (e^{x} + 2) (2 e^{2 x} + 1)

= (e^{x} + 2) (2 e^{2 x} + 1)

p^{2} q - pq r - 2 p r + 2 r^{2}

(\frac{1}{9})^{- 2}

a (x \cdot y)

\cdot (\cdot + 3)

(x + 3)^{2} - 2 (x + 3) + 1

What is factor 2e^{3x}+4e^{2x}+e^x+2 ?
The solution to factor 2e^{3x}+4e^{2x}+e^x+2 is (e^x+2)(2e^{2x}+1)