Find the Degree, Leading Term, and Leading Coefficient (4x-3)^4

${(4 x - 3)}^{4}$

Step 1

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

Use the Binomial Theorem.

${(4 x)}^{4} + 4 {(4 x)}^{3} \cdot - 3 + 6 {(4 x)}^{2} {(- 3)}^{2} + 4 (4 x) {(- 3)}^{3} + {(- 3)}^{4}$

Simplify each term.

Apply the product rule to $4 x$ .

$4^{4} x^{4} + 4 {(4 x)}^{3} \cdot - 3 + 6 {(4 x)}^{2} {(- 3)}^{2} + 4 (4 x) {(- 3)}^{3} + {(- 3)}^{4}$

Raise $4$ to the power of $4$ .

$256 x^{4} + 4 {(4 x)}^{3} \cdot - 3 + 6 {(4 x)}^{2} {(- 3)}^{2} + 4 (4 x) {(- 3)}^{3} + {(- 3)}^{4}$

Apply the product rule to $4 x$ .

$256 x^{4} + 4 (4^{3} x^{3}) \cdot - 3 + 6 {(4 x)}^{2} {(- 3)}^{2} + 4 (4 x) {(- 3)}^{3} + {(- 3)}^{4}$

Multiply $4$ by $4^{3}$ by adding the exponents.

Move $4^{3}$ .

$256 x^{4} + 4^{3} \cdot 4 x^{3} \cdot - 3 + 6 {(4 x)}^{2} {(- 3)}^{2} + 4 (4 x) {(- 3)}^{3} + {(- 3)}^{4}$

Multiply $4^{3}$ by $4$ .

Raise $4$ to the power of $1$ .

$256 x^{4} + 4^{3} \cdot 4^{1} x^{3} \cdot - 3 + 6 {(4 x)}^{2} {(- 3)}^{2} + 4 (4 x) {(- 3)}^{3} + {(- 3)}^{4}$

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

$256 x^{4} + 4^{3 + 1} x^{3} \cdot - 3 + 6 {(4 x)}^{2} {(- 3)}^{2} + 4 (4 x) {(- 3)}^{3} + {(- 3)}^{4}$

Add $3$ and $1$ .

$256 x^{4} + 4^{4} x^{3} \cdot - 3 + 6 {(4 x)}^{2} {(- 3)}^{2} + 4 (4 x) {(- 3)}^{3} + {(- 3)}^{4}$

Raise $4$ to the power of $4$ .

$256 x^{4} + 256 x^{3} \cdot - 3 + 6 {(4 x)}^{2} {(- 3)}^{2} + 4 (4 x) {(- 3)}^{3} + {(- 3)}^{4}$

Multiply $- 3$ by $256$ .

$256 x^{4} - 768 x^{3} + 6 {(4 x)}^{2} {(- 3)}^{2} + 4 (4 x) {(- 3)}^{3} + {(- 3)}^{4}$

Apply the product rule to $4 x$ .

$256 x^{4} - 768 x^{3} + 6 (4^{2} x^{2}) {(- 3)}^{2} + 4 (4 x) {(- 3)}^{3} + {(- 3)}^{4}$

Raise $4$ to the power of $2$ .

$256 x^{4} - 768 x^{3} + 6 (16 x^{2}) {(- 3)}^{2} + 4 (4 x) {(- 3)}^{3} + {(- 3)}^{4}$

Multiply $16$ by $6$ .

$256 x^{4} - 768 x^{3} + 96 x^{2} {(- 3)}^{2} + 4 (4 x) {(- 3)}^{3} + {(- 3)}^{4}$

Raise $- 3$ to the power of $2$ .

$256 x^{4} - 768 x^{3} + 96 x^{2} \cdot 9 + 4 (4 x) {(- 3)}^{3} + {(- 3)}^{4}$

Multiply $9$ by $96$ .

$256 x^{4} - 768 x^{3} + 864 x^{2} + 4 (4 x) {(- 3)}^{3} + {(- 3)}^{4}$

Multiply $4$ by $4$ .

$256 x^{4} - 768 x^{3} + 864 x^{2} + 16 x {(- 3)}^{3} + {(- 3)}^{4}$

Raise $- 3$ to the power of $3$ .

$256 x^{4} - 768 x^{3} + 864 x^{2} + 16 x \cdot - 27 + {(- 3)}^{4}$

Multiply $- 27$ by $16$ .

$256 x^{4} - 768 x^{3} + 864 x^{2} - 432 x + {(- 3)}^{4}$

Raise $- 3$ to the power of $4$ .

$256 x^{4} - 768 x^{3} + 864 x^{2} - 432 x + 81$

Step 2

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

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

$256 x^{4} \to 4$

$- 768 x^{3} \to 3$

$864 x^{2} \to 2$

$- 432 x \to 1$

$81 \to 0$

The largest exponent is the degree of the polynomial.

$4$

Step 3

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

$256 x^{4}$

Step 4

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.

$256 x^{4}$

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

$256$

Step 5

List the results.

Polynomial Degree: $4$

Leading Term: $256 x^{4}$

Leading Coefficient: $256$

Find the Degree, Leading Term, and Leading Coefficient (4x-3)^4

Related Questions

Support LCMGCF.com by disabling your adblocker.