Question

1. f(x) = (x + 1)(x + 3)(x - 4)Standard Form:Degree:Leading coefficient:Constant term:2. g(x) = 3(x + 1)(x + 3)(x - 4)Standard Form:Degree:Leading coefficient:Constant term:

Answer 1

Let's begin by listing out the information given to us:

1.

`\begin{gathered} f\mleft(x\mright)=(x+1)\mleft(x+3\mright)\mleft(x-4\mright) \\ f(x)=(x+1)\cdot x(x-4)+3(x-4) \\ f(x)=(x+1)(x^2-4x+3x-12)\Rightarrow(x+1)(x^2-x-12) \\ f(x)=(x+1)(x^2-x-12)\Rightarrow x(x^2-x-12)+1(x^2-x-12) \\ f(x)=x^3-x^2-12x+x^2-x-12\Rightarrow x^3-13x-12 \\ f(x)=x^3-13x-12 \end{gathered}`

Degree: 3

Leading coefficient: 1

Constant term: -12

2.

`\begin{gathered} g\mleft(x\mright)=3\mleft(x+1\mright)\mleft(x+3\mright)\mleft(x-4\mright) \\ g(x)=3(x^3-13x-12)\Rightarrow3x^3-39x-36 \\ 3x^3-39x-36 \end{gathered}`

Degree: 3

Leading coefficient: 3

Constant term: -36