Question

One factor of f (x ) = 4 x cubed minus 4 x squared minus 16 x + 16 is (x – 2). What are all the roots of the function? Use the Remainder Theorem.

x = 1, x = 2, or x = 4
x = –2, x = 1, or x = 2
x = 2, x = 4, or x = 16
x = –16, x = 2, or x = 16

Answer 1

b -2 2 1

Explanation:

Answer 2

To solve the problem we must know about the Remainder Theorem.

What is the Remainder theorem?

According to the remainder theorem, when a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). If P(t)=0, then the (x-t) is the factor of the polynomial.

The roots of the function are 2, 1, and -2.

Given to us.

One factor of f (x) = is (x – 2).

What is the quotient of the function?

We know (x-2) is the factor of the function, f(x) = ,

therefore,

As (x-2) is the factor of the function, therefore, the remainder will be zero for the equation,

What are the factors of the function?

Solving the quadratic equation,

Hence, the roots of the function are 2, 1, and -2.

Explanation:

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