Given that 2 is a zero of the polynomial function $f (x)$ , find the remaining zeros.
$f (x) = x^{3} - 10 x^{2} + 36 x - 40$
List the remaining zeros (other than 2).
(Simplify your answer. Type an exact answer, using radicals and $i$ as needed. Use a comma to separate answers as needed.)

Answer

Expert–verified

Hide Steps

Answer

Final Answer: The remaining zeros of the polynomial function $f (x) = x^{3} - 10 x^{2} + 36 x - 40$ are $4, 5$ .

Steps

Step 1 ：Given that 2 is a zero of the polynomial function $f (x) = x^{3} - 10 x^{2} + 36 x - 40$ , we can find the remaining zeros by dividing the polynomial by $(x - 2)$ .

Step 2 ：The quotient polynomial is then $x^{2} - 8 x + 20$ .

Step 3 ：We find the zeros of this polynomial by setting it equal to zero and solving for $x$ .

Step 4 ：Solving $x^{2} - 8 x + 20 = 0$ gives us the remaining zeros of the original polynomial.

Step 5 ：Final Answer: The remaining zeros of the polynomial function $f (x) = x^{3} - 10 x^{2} + 36 x - 40$ are $4, 5$ .

Given that 2 is a zero of the polynomial function f(x), find the remaining zeros.f(x)=x3−10x2+36x−40List the remaining zeros (other than 2).(Simplify your answer. Type an exact answer, using radicals and i as needed. Use a comma to separate answers as needed.)

Answer

Popular Problems

Given that 2 is a zero of the polynomial function $f (x)$ , find the remaining zeros.
$f (x) = x^{3} - 10 x^{2} + 36 x - 40$
List the remaining zeros (other than 2).
(Simplify your answer. Type an exact answer, using radicals and $i$ as needed. Use a comma to separate answers as needed.)