SOLUTION: find a polynomial of the specified degree: degree 4, zeros:-5,0,5,7 P(x)=

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1. Put x= before each zero:

x=-5;  x=0,   x=5,   x=7

2. Get 0 on the right of each of the 4 equations:

x+5=0; x=0; x-5=0; x-7=0

3. Indicate that the multiplication (product) of all the left sides equals
the multiplication (product) of all the 0's on the right side, which is just
0.

(x+5)x(x-5)(x-7) = 0

4. Do the multiplication:

To make the mutiplication easier put the x third

(x+5)(x-5)x(x-7) = 0

Multiply the first two that are conjugates (x+5)(x-5)
and distribute the x into the (x-7).

(x²-25)(x²-7x) = 0

Now just use FOIL

x4-7x3-25x2+175x = 0

5. The polynomial P(x) equals the left side of that polynomial equation:

P(x) = x4-7x3-25x2+175x

[Be sure not to put "= 0" after it, for P(x) does not necessarily equal to
0.  P(x) only equals 0 when x equals to one of the 4 given zeros.]

Edwin