Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. -4,1,7

Question

im stuck on multiplying factors

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros

-4,1,7

Answer 1

f(x) = (x-7)(x-1)(x+4) is the desired polynomial having the given zeros; each factor is of the form x - root.

 

The multiplication process should use FOIL, which I hope tht you have learned, on the first two factors;

this gives x² -8x +7 as a quadratic factor, to be multiplied by

x + 4, which (using LONG MULTIPLICATION) gives you these two lines:

 

x³ -8x²    + 7x

    +4x² -32x + 28

 

and when you add these up (notice the columns that are 'alike' you get the final answer.

You can check the results by substituting -4, 1 and 7 in and in each case you should get 0.