Question

secondary math iii // module 3
polynomial functions - 3.10
11.
function in standard form:
function in factored form: ( g(x) = -x(x - 2)(x - 4) )
end behavior:
as ( x \to -infty, g(x) \to )
as ( x \to infty, g(x) \to )
roots (with multiplicity):
degree:
value of leading co - efficient:
12.
function in standard form: ( h(x) = x^3 - 2x^2 - 3x )
function in factored form:
end behavior:
as ( x \to -infty, h(x) \to )
as ( x \to infty, h(x) \to )
roots (with multiplicity):
degree:

Explanation:

Step1: Analyze the function \( g(x) = -x(x - 2)(x - 4) \)

To find the standard form, we expand the factored form. First, multiply \( (x - 2)(x - 4) \):
\( (x - 2)(x - 4)=x^2-4x - 2x + 8=x^2-6x + 8 \)

Step2: Multiply by \(-x\)

Now, multiply \( -x \) with \( x^2-6x + 8 \):
\( g(x)=-x(x^2-6x + 8)=-x^3 + 6x^2-8x \)

Answer:

The standard form of \( g(x) \) is \( -x^3 + 6x^2-8x \)