# Find the Behavior (Leading Coefficient Test) -3(x-1)^2(x^2-4)

Write as a function.
Identify the degree of the function.
Simplify and reorder the polynomial.
Rewrite as .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply by .
Move to the left of .
Rewrite as .
Rewrite as .
Multiply by .
Subtract from .
Apply the distributive property.
Simplify.
Multiply by .
Multiply by .
Expand by multiplying each term in the first expression by each term in the second expression.
Simplify terms.
Simplify each term.
Multiply by by adding the exponents.
Move .
Use the power rule to combine exponents.
Multiply by .
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Multiply by .
Multiply by .
Subtract from .
The largest exponent is the degree of the polynomial.
Since the degree is even, the ends of the function will point in the same direction.
Even
Simplify the polynomial, then reorder it left to right starting with the highest degree term.
Rewrite as .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply by .
Move to the left of .
Rewrite as .
Rewrite as .
Multiply by .
Subtract from .
Apply the distributive property.
Simplify.
Multiply by .
Multiply by .
Expand by multiplying each term in the first expression by each term in the second expression.
Simplify terms.
Simplify each term.
Multiply by by adding the exponents.
Move .
Use the power rule to combine exponents.
Multiply by .
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Multiply by .
Multiply by .
Subtract from .
Move .
The leading term in a polynomial is the term with the highest degree.
The leading coefficient in a polynomial is the coefficient of the leading term.
Since the leading coefficient is negative, the graph falls to the right.
Negative
Use the degree of the function, as well as the sign of the leading coefficient to determine the behavior.
1. Even and Positive: Rises to the left and rises to the right.
2. Even and Negative: Falls to the left and falls to the right.
3. Odd and Positive: Falls to the left and rises to the right.
4. Odd and Negative: Rises to the left and falls to the right
Determine the behavior.
Falls to the left and falls to the right
Find the Behavior (Leading Coefficient Test) -3(x-1)^2(x^2-4)