How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are -2, -4, -7?

1 Answer
Dec 5, 2016

The zeros are: color(red)(-2),color(blue)(-4) and color(green)(-7)

Find the factors of the function in the form of (x+z)

The first factor:-
zcolor(red)(-2)=0
z=2

(x+2)

The second factor:-
zcolor(blue)(-4)=0
z=4

(x+4)

The third factor:-
zcolor(green)(-7)=0
z=7

(x+7)

Multiply the factors to get the least-degree function

(x+2)(x+4)(x+7)=(x^2+4x+2x+8)(x+7)

=(x^2+6x+8)(x+7)

=x^3+7x^2+6x^2+42x+8x+56

Combine like terms

f(x)=x^3+13x^2+50x+56