Write a polynomial function (f) of least degree that has rational coefficients, a leading coefficient of 1, and he given zeros. Write the function in standard form.

Question

The given zeros for the first one are

-4, -2, 5

The next questions zeros are

4, 6, negative square root of 7

The last questions zeros are

0, 5, -5+(square root of) 8

Answer 1

To find to polynomial from zeros.

1. 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)
2. Multiply the factors together.

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

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