One factor of f of x is equal to 4 x cubed minus 4 x squared minus 16 x plus 16 is open paren x minus 2 close paren What are all the roots of the function? Use the Remainder Theorem.

By the Remainder Theorem, the given factor x − 2 means f(2) = 0. Factor the polynomial by grouping: 4x³ − 4x² − 16x + 16 = 4(x − 1)(x² − 4) = 4(x − 1)(x − 2)(x + 2). Setting each factor equal to zero gives the roots x = 1, x = 2, and x = −2, which matches choice A.

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