A (x)=(x-3) (x-4) (3x-7) (4x-3) Whats the leading term and coefficient?

The given polynomial function is:

\[
A(x) = (x - 3)(x - 4)(3x - 7)(4x - 3)
\]

To find the **leading term** and **leading coefficient**, we need to expand the polynomial, focusing on the highest-degree terms.

1. First, multiply the terms inside each pair of parentheses:

\[
(x - 3)(x - 4) = x^2 - 7x + 12
\]
\[
(3x - 7)(4x - 3) = 12x^2 - 37x + 21
\]

2. Now, multiply these two quadratic results together, focusing on the terms that will give the highest degree:

\[
(x^2 - 7x + 12)(12x^2 - 37x + 21)
\]

For the highest degree term, multiply the leading terms \(x^2\) from the first quadratic and \(12x^2\) from the second:

\[
x^2 \cdot 12x^2 = 12x^4
\]

Thus, the **leading term** is \(12x^4\) and the **leading coefficient** is **12**.

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Would you like more details on expanding the entire polynomial?

Here are 5 related questions to consider:
1. How can you expand the entire polynomial step by step?
2. What are the other coefficients of the polynomial after full expansion?
3. How do you factor a polynomial after full expansion?
4. How does the degree of the polynomial affect its graph?
5. What happens to the end behavior of the polynomial given the leading coefficient?

**Tip**: Always focus on the highest-degree terms when determining the leading term of a polynomial.

A (x) = (x-3)(x-4)(3x-7)(4x-3) What is the leading term and coefficient?

Explore how to find the leading term and coefficient of the polynomial (x - 3)(x - 4)(3x - 7)(4x - 3). This problem involves expanding quadratics and focusing on the highest degree terms. Suitable for Grades 10-12 students, this solution breaks down each step, applying key algebraic principles.

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