Question

If f(2)=0 and f(-1)=0 then which of the following must be a factor of f(x)? a) x+2 b) x-1 c)`x^2+x-2` d) `x^2-x-2` e) none of these

Answer 1

`"see explanation"`

Explanation:

`"using the "color(blue)"factor theorem"`

`"If "f(a)=0" then "(x-a)" is a factor of "f(x)`

`"here "f(2)=0" and "f(-1)=0`

`rArr(x-2)" and "(x+1)" are factors of "f(x)`

`rArrf(x)=k(x-2)(x+1)larrcolor(blue)"k is a multiplier"`

`"let k = 1"`

`rArrf(x)=x^2-x-2`

`rArr"factor of "f(x)" is "x^2-x-2to(d)`