Answer:
a) factors of polynomial are: (x+1)(x-2)(x-5)
b) the required polynomial in standard form is: [tex]\mathbf{x^3-6x^2+3x+10}[/tex]
Step-by-step explanation:
The polynomial has zeros at -1,2,5
Part A) Write the three factors of the polynomial
we have x=-1, x=2 and x=5 as zeros of polynomial
so factors will be:
(x+1)=0, (x-2)=0, (x-5)=0
So, factors of polynomial are: (x+1)(x-2)(x-5)
Part B) Write the polynomial in standard form
For finding polynomial, we will multiply all the factors i.e
(x+1)(x-2)(x-5)
[tex](x+1)(x-2)(x-5)\\=(x(x-2)+1(x-2))(x-5)\\=(x^2-2x+x-2)(x-5)\\=(x^2-x-2)(x-5)\\=x(x^2-x-2)-5(x^2-x-2)\\=x^3-x^2-2x-5x^2+5x+10\\=x^3-x^2-5x^2+5x-2x+10\\=x^3-6x^2+3x+10[/tex]
So, the required polynomial in standard form is: [tex]x^3-6x^2+3x+10[/tex]
