# How do you factor #2c^2 + 4cd + 3c + 3d#?

##### 1 Answer

Nov 17, 2015

This does not factor into linear factors.

#### Explanation:

Suppose:

#2c^2+4cd+3c+3d = (pc+qd+r)(sc+td+u)#

for some

Then

#2c^2+4cd+3c+3d = (pc+qd+r)(sc+td)#

Next looking at the coefficient of

#2c^2+4cd+3c+3d = (pc+r)(sc+td)#

Looking at the coefficients of

So

#2c^2+4cd+3c+3d = s(pc+r)(c+d)#

Then looking at the coefficients of

#2 = sp = 4#

which is false.

So there is no such linear factorisation.