Answer:
Rewriting p(x) as a product of linear factors: [tex]\mathbf{f(x)=(x+3)(x-2)(x+6)}[/tex]
Step-by-step explanation:
The polynomial [tex]p(x) = x^3 + 7x^2 - 36[/tex] has a known factor of [tex](x + 3)[/tex]
We need to find other factors.
First we find quotient of [tex]p(x) = x^3 + 7x^2 - 36[/tex] divided by [tex](x + 3)[/tex]
The division is shown in image attached.
The quotient is: [tex]x^2+4x-12[/tex]
Now, factoring the quotient [tex]x^2+4x-12[/tex]
[tex]x^2+4x-12\\=x^2+6x-2x-12\\=x(x+6)-2(x+6)\\=(x-2)(x+6)[/tex]
The other two factors are (x-2)(x+6)
So, Rewriting p(x) as a product of linear factors: [tex]f(x)=(x+3)(x-2)(x+6)[/tex]
