What is factor 2^{2x}+3(2^x)-18 ?

The solution to factor 2^{2x}+3(2^x)-18 is (2^x-3)(2^x+6)

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factor 2^{2x}+3(2^x)-18

factor

2^{2 x} + 3 (2^{x}) - 18

(2^{x} - 3) (2^{x} + 6)

Solution steps

2^{2 x} + 3 (2^{x}) - 18

Apply exponent rule:

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

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

= (2^{x})^{2} + 3 (2^{x}) - 18

Write in the standard form

a x^{2} + b x + c

= (2^{x})^{2} + 3 2^{x} - 18

Break the expression into groups

= ((2^{x})^{2} - 3 2^{x}) + (6 2^{x} - 18)

Factor out

2^{x}

from

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

Factor out

6

from

6 2^{x} - 18 : 6 (2^{x} - 3)

= 2^{x} (2^{x} - 3) + 6 (2^{x} - 3)

Factor out common term

2^{x} - 3

= (2^{x} - 3) (2^{x} + 6)

1 + (sin (θ))^{2}

x^{2} - 0.25

(x - 3)^{3} + 125

e^{- 2 t} u (t) + e^{3 t} u (- t)

x^{2} - 12 + 35

What is factor 2^{2x}+3(2^x)-18 ?
The solution to factor 2^{2x}+3(2^x)-18 is (2^x-3)(2^x+6)