Find the Degree, Leading Term, and Leading Coefficient f(t)=3t(t-3)(t+4)

$f (t) = 3 t (t - 3) (t + 4)$

Simplify the polynomial, then reorder it left to right starting with the highest degree term.

Apply the distributive property.

$f (t) = 3 t (t - 3) t + 3 t (t - 3) \cdot 4$

Simplify the expression.

Multiply $4$ by $3$ .

$f (t) = 3 t (t - 3) t + 12 t (t - 3)$

Reorder factors in $3 t (t - 3) t + 12 t (t - 3)$ .

$f (t) = 3 t \cdot t (t - 3) + 12 t (t - 3)$

The degree of a polynomial is the highest degree of its terms.

Simplify and reorder the polynomial.

Simplify each term.

Multiply $t$ by $t$ by adding the exponents.

Move $t$ .

$3 (t \cdot t) (t - 3) + 12 t (t - 3)$

Multiply $t$ by $t$ .

$3 t^{2} (t - 3) + 12 t (t - 3)$

Apply the distributive property.

$3 t^{2} t + 3 t^{2} \cdot - 3 + 12 t (t - 3)$

Multiply $t^{2}$ by $t$ by adding the exponents.

Move $t$ .

$3 (t \cdot t^{2}) + 3 t^{2} \cdot - 3 + 12 t (t - 3)$

Multiply $t$ by $t^{2}$ .

Raise $t$ to the power of $1$ .

$3 (t^{1} t^{2}) + 3 t^{2} \cdot - 3 + 12 t (t - 3)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 t^{1 + 2} + 3 t^{2} \cdot - 3 + 12 t (t - 3)$

Add $1$ and $2$ .

$3 t^{3} + 3 t^{2} \cdot - 3 + 12 t (t - 3)$

Multiply $- 3$ by $3$ .

$3 t^{3} - 9 t^{2} + 12 t (t - 3)$

Apply the distributive property.

$3 t^{3} - 9 t^{2} + 12 t \cdot t + 12 t \cdot - 3$

Multiply $t$ by $t$ by adding the exponents.

Move $t$ .

$3 t^{3} - 9 t^{2} + 12 (t \cdot t) + 12 t \cdot - 3$

Multiply $t$ by $t$ .

$3 t^{3} - 9 t^{2} + 12 t^{2} + 12 t \cdot - 3$

Multiply $- 3$ by $12$ .

$3 t^{3} - 9 t^{2} + 12 t^{2} - 36 t$

Add $- 9 t^{2}$ and $12 t^{2}$ .

$3 t^{3} + 3 t^{2} - 36 t$

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

$3 t^{3} \to 3$

$3 t^{2} \to 2$

$- 36 t \to 1$

The largest exponent is the degree of the polynomial.

$3$

The leading term of a polynomial is the term with the highest degree.

Simplify the polynomial, then reorder it left to right starting with the highest degree term.

Simplify each term.

Multiply $t$ by $t$ by adding the exponents.

Move $t$ .

$3 (t \cdot t) (t - 3) + 12 t (t - 3)$

Multiply $t$ by $t$ .

$3 t^{2} (t - 3) + 12 t (t - 3)$

Apply the distributive property.

$3 t^{2} t + 3 t^{2} \cdot - 3 + 12 t (t - 3)$

Multiply $t^{2}$ by $t$ by adding the exponents.

Move $t$ .

$3 (t \cdot t^{2}) + 3 t^{2} \cdot - 3 + 12 t (t - 3)$

Multiply $t$ by $t^{2}$ .

Raise $t$ to the power of $1$ .

$3 (t^{1} t^{2}) + 3 t^{2} \cdot - 3 + 12 t (t - 3)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 t^{1 + 2} + 3 t^{2} \cdot - 3 + 12 t (t - 3)$

Add $1$ and $2$ .

$3 t^{3} + 3 t^{2} \cdot - 3 + 12 t (t - 3)$

Multiply $- 3$ by $3$ .

$3 t^{3} - 9 t^{2} + 12 t (t - 3)$

Apply the distributive property.

$3 t^{3} - 9 t^{2} + 12 t \cdot t + 12 t \cdot - 3$

Multiply $t$ by $t$ by adding the exponents.

Move $t$ .

$3 t^{3} - 9 t^{2} + 12 (t \cdot t) + 12 t \cdot - 3$

Multiply $t$ by $t$ .

$3 t^{3} - 9 t^{2} + 12 t^{2} + 12 t \cdot - 3$

Multiply $- 3$ by $12$ .

$3 t^{3} - 9 t^{2} + 12 t^{2} - 36 t$

Add $- 9 t^{2}$ and $12 t^{2}$ .

$3 t^{3} + 3 t^{2} - 36 t$

The leading term in a polynomial is the term with the highest degree.

$3 t^{3}$

The leading coefficient of a polynomial is the coefficient of the leading term.

The leading term in a polynomial is the term with the highest degree.

$3 t^{3}$

The leading coefficient in a polynomial is the coefficient of the leading term.

$3$

List the results.

Polynomial Degree: $3$

Leading Term: $3 t^{3}$

Leading Coefficient: $3$

Find the Degree, Leading Term, and Leading Coefficient f(t)=3t(t-3)(t+4)

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