What is the completely factored form of f(x)=x^3+4x^2+7x+6? f(x)=(x+2)(x−(−3+i10−−√−(−3−i10−−√) ) f(x)=(x+2)(x−(−1+i2√−(−1−i2√)) f(x)=(x−2)(x−(−1+i2√−(−1−i2√)) f(x)=(x−2)(x−(−3+i10−−√−(−3−i10−−√) )

we are given

We will use rational root theorem to find factors

We can see that

Leading coefficient =1

constant term is 6

so, we will find all possible factors of 6

now, we will check each terms

At x=-2:

We can use synthetic division

we get

so, x+2 will be factor

and we can write our expression from synthetic division as

now, we can find factor of remaining terms

we can use quadratic formula

we can compare our equation with quadratic equation

we get

now, we can plug these values

so, we get

so, we can write factor as

so, we get completely factored form as

...............Answer

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