The problem asks to rewrite the polynomial in standard form and to state its degree and constant term. Let's solve the part b of the question for the given polynomial:

$g(x) = 3(x+1)(x+3)(x-4)$

Step 1: Expand the polynomial

First, expand $(x+1)(x+3)$: $(x+1)(x+3) = x^2 + 3x + x + 3 = x^2 + 4x + 3$

Now, multiply this by $(x-4)$: $(x^2 + 4x + 3)(x-4) = x^2(x-4) + 4x(x-4) + 3(x-4)$ $= x^3 - 4x^2 + 4x^2 - 16x + 3x - 12$ $= x^3 - 13x - 12$

Step 2: Multiply by the constant 3

Now, multiply everything by 3: $g(x) = 3(x^3 - 13x - 12) = 3x^3 - 39x - 36$

Final Result:

The polynomial in standard form is: $g(x) = 3x^3 - 39x - 36$

Degree and Constant Term:

• Degree: The highest power of $x$ is 3, so the degree of the polynomial is 3.
• Constant Term: The constant term is $-36$.

Would you like further clarification or have any other questions?

Here are five related questions for further practice:

1. How would you expand a polynomial with four terms in the product?
2. What is the leading coefficient of $g(x)$?
3. Can you factor the expanded form back into its factored form?
4. What happens to the degree of a polynomial when multiplied by a constant?
5. How do you determine the constant term when given a factored form?

Tip: Always check the expanded terms carefully for any sign errors when multiplying polynomials!