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sExample 6. Without nctual dieision, prove that 2x+ x 2x 2 is divisible byINCERT Exemplar) |
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Answer» First of all, x^2-3x+2=>x^2-2x-1x+2=>x(x-2)-1(x-2)=>(x-2)(x-1)Therefore,(x-2)(x-1)are the factors.i) (x-2)x-2=0=>x=2So,p(x)=2p(x)=2x^4-5x^3+2x^2-x+2p(2)=2(2)^4-5(2)^3+2(2)^2-2+2=32-40+8= -40+40=0Hence,it proves that (x-2) is a factor .ii) (x-1)=>x-1=0=>x=1So,p(x)=1p(x)=2x^4-5x^3+2x^2-x+2p(1)=2(1)^4-5(1)^3+2(1)^2-1+2=2-5+2-1+2=6-6=0Hence,it proves that (x-1) is a factor. Like my answer if you find it useful! |
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