Question

1. create a polynomial equation in factored form having roots: -5, 1, and 4 with multiplicity of 3? multiplicity means: the polynomial has more than one of that factor work backwards now show as factors switch signs. f(x)=

Explanation:

Step1: Use the root - factor relationship

If \(r\) is a root of a polynomial, then \((x - r)\) is a factor. For root \(r=-5\), the factor is \((x+5)\); for root \(r = 1\), the factor is \((x - 1)\); for root \(r=4\), the factor is \((x - 4)\)

Step2: Apply multiplicity

Since the multiplicity of each root is \(3\), the polynomial in factored form is \(f(x)=(x + 5)^{3}(x - 1)^{3}(x - 4)^{3}\)

Answer:

\(f(x)=(x + 5)^{3}(x - 1)^{3}(x - 4)^{3}\)