Factoring Trig Expressions

Factor out the GCF: $12\sin\theta-60$ 

•  $2\left(6\sin\theta-30\right)$  

•  $3\left(4\sin\theta-20\right)$  

•  $6\left(2\sin\theta-10\right)$  

•  $12\left(\sin\theta-5\right)$  

Factor out the GCF: $\cos^2\theta-5\cos\theta$  

•  $\cos\theta\left(\cos\theta-5\cos\theta\right)$  

•  $\cos\theta\left(\cos^2\theta-5\cos\theta\right)$  

•  $\cos\theta\left(\cos\theta-5\right)$  

•  $\cos^2\theta\left(\cos\theta-5\right)$  

Factor out the GCF: $8\cot^2\theta+20\cot\theta$  

•  $2\left(4\cot^2\theta+10\cot\theta\right)$  

•  $2\cot\theta\left(4\cot\theta+10\right)$  

•  $4\left(\cot^2\theta+5\cot\theta\right)$  

•  $4\cot\theta\left(2\cot\theta+5\right)$  

Factor out the GCF: $21\sec^3\theta+9\sec^2\theta$  

•  $3\sec^2\theta\left(7\sec\theta+3\right)$  

•  $\sec^2\theta\left(21\sec\theta+9\right)$  

•  $3\sec\theta\left(7\sec^2\theta+3\sec\theta\right)$  

•  $\sec\theta\left(21\sec^2\theta+9\sec\theta\right)$  

Factor out the GCF: $12\cos\theta\cot\theta-16\cos\theta$  

•  $\cos\theta\left(12\cot\theta-16\right)$  

•  $2\cos\theta\left(6\cot\theta-8\right)$  

•  $4\cos\theta\left(3\cot\theta-4\right)$  

•  $6\cos\theta\left(2\cot\theta-3\right)$  

Factor the trinomial into its binomial factors: $\csc^2\theta-2\csc\theta-24$ 

•  $\left(\csc\theta+4\right)\left(\csc\theta-6\right)$  

•  $\left(\csc\theta+4\right)\left(\csc\theta+6\right)$  

•  $\left(\csc\theta+6\right)\left(\csc\theta-1\right)$  

•  $\left(\csc\theta-4\right)\left(\csc\theta+6\right)$  

Factor the trinomial into its binomial factors: $\tan^2\theta+11\tan\theta+30$  

•  $\left(\tan\theta+1\right)\left(\tan\theta+30\right)$  

•  $\left(\tan\theta+2\right)\left(\tan\theta+15\right)$  

•  $\left(\tan\theta+3\right)\left(\tan\theta+10\right)$  

•  $\left(\tan\theta+5\right)\left(\tan\theta+6\right)$  

Factor the trinomial into its binomial factors: $\sec^2\theta+11\sec\theta-60$  

•  $\left(\sec\theta+12\right)\left(\sec-5\right)$  

•  $\left(\sec\theta+10\right)\left(\sec\theta+6\right)$  

•  $\left(\sec\theta+15\right)\left(\sec\theta-4\right)$  

•  $\left(\sec\theta-3\right)\left(\sec\theta-20\right)$  

Factor the trinomial into its binomial factors:  $\cos^2\theta-16\cos\theta+64$  

•  $\left(\cos\theta+4\right)\left(\cos\theta+16\right)$  

•  $\left(\cos\theta-8\right)\left(\cos\theta-8\right)$  

•  $\left(\cos\theta+2\right)\left(\cos\theta+32\right)$  

•  $\left(\cos\theta+8\right)\left(\cos\theta+8\right)$  

Factor completely (this is a two step factoring problem - you must factor out the GCF first, then the trinomial inside): $2\sec^3\theta+6\sec^2\theta-20\sec\theta$  

•  $\sec\theta\left(2\sec^2\theta+6\sec\theta-20\right)$  

•  $2\sec\theta\left(\sec^2\theta+3\sec\theta-10\right)$  

•  $\sec\theta\left(2\sec+10\right)\left(\sec\theta-2\right)$  

•  $2\sec\theta\left(\sec\theta+5\right)\left(\sec\theta-2\right)$