What is factor e^{2x}-8e^x+15 ?

The solution to factor e^{2x}-8e^x+15 is (e^x-3)(e^x-5)

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factor e^{2x}-8e^x+15

factor

e^{2 x} - 8 e^{x} + 15

(e^{x} - 3) (e^{x} - 5)

Solution steps

e^{2 x} - 8 e^{x} + 15

Apply exponent rule:

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

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

= (e^{x})^{2} - 8 e^{x} + 15

Break the expression into groups

= ((e^{x})^{2} - 3 e^{x}) + (- 5 e^{x} + 15)

Factor out

e^{x}

from

(e^{x})^{2} - 3 e^{x} : e^{x} (e^{x} - 3)

Factor out

- 5

from

- 5 e^{x} + 15 : - 5 (e^{x} - 3)

= e^{x} (e^{x} - 3) - 5 (e^{x} - 3)

Factor out common term

e^{x} - 3

= (e^{x} - 3) (e^{x} - 5)

[1 - sin (a)] [1 + sin (a)]

2 x^{2} + 7 x^{2} + 2 x - 3

\frac{9 x ^{2} - 25}{6 x - 15}

\frac{x ^{2} + 5 x - 24}{x - 3}

2 x + 3 y + 8 x z + 12 zy

What is factor e^{2x}-8e^x+15 ?
The solution to factor e^{2x}-8e^x+15 is (e^x-3)(e^x-5)