Question

PLEASE HELP!
how would you factor 4cos^2(x) - 2sqroot2 cos(x) + 2cos(x) - sqroot 2 = 0 into...
(sqroot2 - 2cos(x) ) ( 2cos(x) + 1) ?

Answer 1

\[4\cos ^2\left(x\right)-2\sqrt{2}\cos \left(x\right)+2\cos \left(x\right)-\sqrt{2}=0\]\[\left(\sqrt{2}-2\cos \left(x\right)\right)\left(2\cos \left(x\right)+1\right)=0\]

Answer 2

\[4\cos ^2\left(x\right)-2\sqrt{2}\cos \left(x\right)+2\cos \left(x\right)-\sqrt{2}\]Rearrage the terms\[=4\cos ^2\left(x\right)+2\cos \left(x\right)-2\sqrt{2}\cos \left(x\right)-\sqrt{2}\]Factorize the first two terms by grouping: \[=2\cos\left(x\right)(2\cos \left(x\right)+1)-2\sqrt{2}\cos \left(x\right)-\sqrt{2}\]Then factorize the last two terms by grouping. Can you give it a try?

Answer 3

\[=2\cos(x)(2\cos(x)+1)−√2(2\cos(x)+1)\]

Answer 4

Yes :)
Now, do factor by grouping again.

Answer 5

\[(2\cos(x)−√2)(2\cos(x)+1)\]

Answer 6

Thank you so much! :)

Answer 7

Welcome :)