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

Question

-5,-1,2

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 -5,-1 and 2 would be:

1. Find the factors: (x+5)(x+1)(x-2)
2.  Multiply the factors together: Will start out with FOIL for (x+5)(x+1) = x² +5x+x+5 = x² +6x+5

Then multiply by the last factor using the distributive property.

(x-2) (x² +6x+5) = x(x²)+x(6x)+x(5)-2(x²)-2(6x)-2(5)

Simplify: x³+6x²+5x-2x²-12x-10

Combine like terms:

x³+4x²-7x-10