Find the Degree (2x-1)(4x^2+3)

$(2 x - 1) (4 x^{2} + 3)$

Simplify and reorder the polynomial.

Expand $(2 x - 1) (4 x^{2} + 3)$ using the FOIL Method.

Apply the distributive property.

$2 x (4 x^{2} + 3) - 1 (4 x^{2} + 3)$

Apply the distributive property.

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

Apply the distributive property.

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

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $2$ by $4$ .

$8 x^{3} + 2 x \cdot 3 - 1 (4 x^{2}) - 1 \cdot 3$

Multiply $3$ by $2$ .

$8 x^{3} + 6 x - 1 (4 x^{2}) - 1 \cdot 3$

Multiply $4$ by $- 1$ .

$8 x^{3} + 6 x - 4 x^{2} - 1 \cdot 3$

Multiply $- 1$ by $3$ .

$8 x^{3} + 6 x - 4 x^{2} - 3$

The largest exponent is the degree of the polynomial.

$3$