Find the Degree, Leading Term, and Leading Coefficient y=(x-1)(4x+2)-4x^2

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

Step 1

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

Simplify each term.

Expand $(x - 1) (4 x + 2)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

Move $2$ to the left of $x$ .

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

Multiply $4$ by $- 1$ .

$y = 4 x^{2} + 2 x - 4 x - 1 \cdot 2 - 4 x^{2}$

Multiply $- 1$ by $2$ .

$y = 4 x^{2} + 2 x - 4 x - 2 - 4 x^{2}$

Subtract $4 x$ from $2 x$ .

$y = 4 x^{2} - 2 x - 2 - 4 x^{2}$

Combine the opposite terms in $4 x^{2} - 2 x - 2 - 4 x^{2}$ .

Subtract $4 x^{2}$ from $4 x^{2}$ .

$y = - 2 x - 2 + 0$

Add $- 2 x - 2$ and $0$ .

$y = - 2 x - 2$

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.

$- 2 x \to 1$

$- 2 \to 0$

The largest exponent is the degree of the polynomial.

$1$

Step 3

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

$- 2 x$

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.

$- 2 x$

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

$- 2$

Step 5

List the results.

Polynomial Degree: $1$

Leading Term: $- 2 x$

Leading Coefficient: $- 2$

Find the Degree, Leading Term, and Leading Coefficient y=(x-1)(4x+2)-4x^2

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