For the polynomial function \(f(x)=x^3-2x^2-5x+6\), we have \(f(0)=6, f(2)=\text-4, f(\text-2)=0, f(3)=0,f(\text-1)=8, f(1)=0\). Rewrite \(f(x)\) as a product of linear factors.
Problem 2
Select all the polynomials that have \((x-4)\) as a factor.
\(x^3-13x-12\)
\(x^3 + 8x^2 + 19x + 12\)
\(x^3+6x^2 + 5x - 12\)
\(x^3-x^2-10x-8\)
\(x^2-4\)
Problem 3
Write a polynomial function, \(p(x)\), with degree 3, that has \(p(7) = 0\).
Problem 4
Long division was used here to divide the polynomial function \(p(x)=x^3+7x^2-20x-110\) by \((x-5)\) and to divide it by \((x+5)\).
We know these things about a polynomial function \(f\): It has degree 3, the leading coefficient is negative, and it has zeros at \(x=\text-5,\text-1, 3\). Sketch a graph of \(f\) given this information.