Question

Factorise: 5(2^n)+2^n+2

Answer 1

2 ( n + 2 ) ( n + 1 2 )

Explanation:

coefficient of the first term:

2 = 2 × 1

coefficient of the last term:

2 = 2 × 1

coefficient of the middle term (using only the factors above):

5 = 2 × 2 + 1 × 1

2 n 2 + 5 n + 2 = ( 2 n + 1 ) ( n + 2 )

Alternative method:

Treat the given expression as a quadratic set equal to zero, with the form

a n 2 + b n + c

and use the quadratic formula

− b ± √ b 2 − 4 a c 2 a

This will given solutions

n = − 2 and n = − 1 2

for a factoring

2 ( n + 2 ) ( n + 1 2 )

Hope this helped