Question: To show that x-2 is a factor of f(x)= 2x3-3x2-17x+30 and also to factorise it
Answer : we have to showthat x-2 is a factor of f(x)= 2x3-3x2-17x+30
Let's put x =2 in f(x) , if the remainder comes out to be 0 then x-2 will be the factor of f(x)
f(2)=2(2)3-3(2)2-17(2)+30
f(2)=2(8)-3(4)-34+30 = 16-12-34+30 = -46+46 = 0
hence x-2 is a factor of f(x)
Now to factorise f(x)
now we do long division of2x3-3x2-17x+30 , which is divided by x-2
we get 2x2+x-15
f(x)= (x-2)(2x2+x-15)
f(x)= (x-2)(2x2+6x-5x-15)
f(x)= (x-2)[2x(x+3)-5(x+3)]
f(x)= (x-2)(2x-5)(x+3) - Answer
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