Factor each polynomial completely?

Question

Factor each polynomial completely
2a2 – 4a – 2

t2 – 9w2

Completely?

Answer 1

2a2 – 4a – 2 I wonder if this is a typo & should be 2a^2-4a+2=2(a+1)(a-1)
2(a^2-2a-1)
2(a-1-sqrt(2))(a-1+sqrt(2))

t2 – 9w2
(t+3w)(t-3w)

Answer 2

The complete factorization of the following polynomials are as follows:

(a) 2a^2 - 4a - 2 = 2(a^2 - 2a - 1)
Note that the polynomial expression a^2 - 2a - 1 is already prime, i.e., a^2 - 2a - 1 is not factorable, whenever a is an integer.

(b) t^2 - 9w^2 = (t - 3w)(t + 3w)

Answer 3

2a^2 - 4a - 2 = 2(a^2 - 2a - 1) = 2(a - 1+sqrt(2))(a - 1-sqrt(2)).

t^2 - 9w^2 = (t+3w)(t-3w)

Answer 4

2(a^2-2a-1)
=2(a-1-sqrt(2))(a-1+sqrt(2))

t^2 - 9w^2 = (t+3w)(t-3w)