1. **Problem Statement:** Complete the chart for each polynomial function by simplifying, finding the degree, and the leading coefficient. 2. **Function a:** $f(x) = (4x + 2)(x - 3)(x + 10)$ 3. **Step 1: Simplify $f(x)$** - First, multiply $(x - 3)(x + 10)$: $$ (x - 3)(x + 10) = x^2 + 10x - 3x - 30 = x^2 + 7x - 30 $$ - Next, multiply $(4x + 2)$ by the result: $$ (4x + 2)(x^2 + 7x - 30) = 4x(x^2 + 7x - 30) + 2(x^2 + 7x - 30) $$ $$ = 4x^3 + 28x^2 - 120x + 2x^2 + 14x - 60 $$ - Combine like terms: $$ 4x^3 + (28x^2 + 2x^2) + (-120x + 14x) - 60 = 4x^3 + 30x^2 - 106x - 60 $$ 4. **Step 2: Degree of $f(x)$** - The degree is the highest power of $x$, which is 3. 5. **Step 3: Leading coefficient of $f(x)$** - The coefficient of the highest degree term $4x^3$ is 4. 6. **Function b:** $g(x) = 3x(1 + x) + 3x^2$ 7. **Step 1: Simplify $g(x)$** - Distribute $3x$: $$ 3x(1 + x) = 3x + 3x^2 $$ - Add $3x^2$: $$ 3x + 3x^2 + 3x^2 = 3x + 6x^2 $$ 8. **Step 2: Degree of $g(x)$** - The highest power of $x$ is 2. 9. **Step 3: Leading coefficient of $g(x)$** - The coefficient of $6x^2$ is 6. **Final answers:** - $f(x) = 4x^3 + 30x^2 - 106x - 60$, degree 3, leading coefficient 4. - $g(x) = 6x^2 + 3x$, degree 2, leading coefficient 6.