# How do you factor the trinomial # 49x^2 − 8x + 16#?

##### 2 Answers

Dec 22, 2015

You use the formula :

Dec 23, 2015

Use the quadratic formula to find:

#49x^2-8x+16#

#= (x-4/49-(16sqrt(3)i)/49)(x-4/49+(16sqrt(3)i)/49)#

#### Explanation:

This has discriminant

#Delta = b^2-4ac = (-8)^2-(4xx49xx16) = 64-3136 = -3072#

#= -3*2^10#

Since this is negative, our trinomial has no linear factors with Real coefficients.

It has Complex zeros given by the quadratic formula:

#x = (-b+-sqrt(b^2-4ac))/(2a) = (8+-sqrt(Delta))/98#

#=(8+-32sqrt(3)i)/98 = (4+-16sqrt(3)i)/49#

Hence:

#49x^2-8x+16#

#= (x-4/49-(16sqrt(3)i)/49)(x-4/49+(16sqrt(3)i)/49)#