Will an extender help increase signal strength

yes and no. A range extender can help. Problem is that range extenders by their very nature reduce throughput and increase latency. Reason why is that they have to recieve and retransmit the signal. So bandwidth is cut in half and it increases latency. so it basically drops your speed to what she's getting.

the tri-band extenders reduce the loss quite a bit but you can still get a little loss.  

but you might be better off investing the $ in centrally locating the router if possible. That many times provides the coverage needed without taking the hit from extenders.