Find a polynomial of the specified degree that has the given zeros.
Degree 4; zeros $-1,1,2,5$
Answer
The polynomial of degree 4 that has the given zeros -1,1,2,5 is \(\boxed{(x - 5)(x - 2)(x - 1)(x + 1)}\).
Step 1 ：The zeros of a polynomial are the values of x for which the polynomial equals zero. If we know the zeros of a polynomial, we can construct the polynomial by multiplying together terms of the form \((x - zero)\). In this case, the zeros are -1, 1, 2, and 5.
Step 2 ：We can construct the polynomial by multiplying together the terms \((x - (-1))\), \((x - 1)\), \((x - 2)\), and \((x - 5)\). This will give us a polynomial of degree 4, as required.
Step 3 ：The polynomial of degree 4 that has the given zeros -1,1,2,5 is \(\boxed{(x - 5)(x - 2)(x - 1)(x + 1)}\).
