Write a polynomial function of f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros: − 2, 1 + √7

To find to polynomial from zeros.

Find the factors. If it is a positive zero, the factor will be (x- zero) If it is a negative zero if is (x+zero)

Multiply the factors together.

Zeros of -4, -2, 5 would be:

Find the factors: (x+4)(x+2)(x-5)

Multiply the factors together: Will start out with FOIL for (x+4)(x+2) = x2+2x+4x+8 Combine like terms. Then multiply by the last factor

(x2+6x+8)(x-5) using the distributive property

x3+6x2+8x-5x2-30x-40 Combine like terms

x3+x2-22x-40

For the next one, the factors are a bit more complicated because of the radical.  With a radical, you will also have to have a factor with the conjugate (Same term opposite sign)

4, 6, negative square root of 7

Factors would be:  (x-4)(x-6)(x-√7)(x+√7)  You can FOIL the first 2 factors and the last 2, then multiply them together using the distributive property.



Step-by-step explanation: