Answer:
The standard form is: [tex]h(x) = 8x^3 - 4x^2 - 10x - 3[/tex]
The function is of the 3rd degree.
The leading coefficient is 8.
The constant term is -3.
Step-by-step explanation:
Placing in standard form:
To place in standard form, we solve the operations. So
[tex]h(x) = (2x+1)^2(2x-3)[/tex]
[tex]h(x) = (4x^2 + 4x + 1)(2x - 3)[/tex]
[tex]h(x) = 8x^3 - 12x^2 + 8x^2 - 12x + 2x - 3[/tex]
[tex]h(x) = 8x^3 - 4x^2 - 10x - 3[/tex]
Degree:
The degree is given by the highest power of x, which, in this exercise, is 3.
Leading coefficient:
The leading coefficient is the term that multiplies the highest power of x. In this exercise, the higher power of x is [tex]x^3[/tex], which is multiplied by 8. So the leading coefficient is 8.
Constant term:
The constant term is the one which does not multiply a power of x. So in this exercise, it is -3.
