How do you factor and simplify 3cot^2x+6cotx+3?

1 Answer
Jim G.
Sep 30, 2016

3(cotx+1)^2

Explanation:

Begin by taking out a color(blue)"common factor" of 3.

rArr3(cot^2x+2cotx+1)

inside the bracket we have a quadratic in cotx.

let x=cotx" then we can write"

3(cot^2x+2cotx+1)=3(x^2+2x+1)

and factorising x^2+2x+1" using the a-c method"

x^2+2x+1=(x+1)(x+1)=(x+1)^2

Replacing x by cotx to obtain.

(x+1)^2=(cotx+1)^2

rArr3cot^2x+6cotx+3=3(cotx+1)^2

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