Question

How do you factor the trinomial `2x^2+ 6x+4`?

Answer 1

It is `2*(x+1)*(x+2)`

Explanation:

Rewrite this as follows

`2x^2+2x+4x+4=2x(x+1)+4(x+1)=(x+1)*(2x+4)= 2*(x+1)*(x+2)`

Answer 2

2(x+1 )(x + 2 )

Explanation:

The standard form of a quadratic function is `ax^2 + bx + c`

To factor , consider the factors of the product ac , which sum to b , the coefficient of the x-term.

for `2x^2 + 6x + 4 : a = 2 , b = 6 , c = 4`

hence ac = `2xx4 = 8 " and " 2 + 4 = 6`

now rewrite 6x as 2x + 4x

becomes : `2x^2 + 2x + 4x + 4`

factor each 'pair' : `2x^2 + 2x = 2x(x + 1 ) " and " 4x + 4 = 4(x+1)`

' take out' common factor of (x + 1 ) : (x + 1 )(2x + 4 )

'take out ' common factor of 2 : (x + 1 ).2(x + 2 )

`rArr 2x^2 + 6x + 4 = 2(x + 1 )(x + 2 )`