Find the Degree, Leading Term, and Leading Coefficient y=(x-5)(5x+4)-5x^2

$y = (x - 5) (5 x + 4) - 5 x^{2}$

Step 1

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

Simplify each term.

Expand $(x - 5) (5 x + 4)$ using the FOIL Method.

Apply the distributive property.

$y = x (5 x + 4) - 5 (5 x + 4) - 5 x^{2}$

Apply the distributive property.

$y = x (5 x) + x \cdot 4 - 5 (5 x + 4) - 5 x^{2}$

Apply the distributive property.

$y = x (5 x) + x \cdot 4 - 5 (5 x) - 5 \cdot 4 - 5 x^{2}$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$y = 5 x \cdot x + x \cdot 4 - 5 (5 x) - 5 \cdot 4 - 5 x^{2}$

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

Move $x$ .

$y = 5 (x \cdot x) + x \cdot 4 - 5 (5 x) - 5 \cdot 4 - 5 x^{2}$

Multiply $x$ by $x$ .

$y = 5 x^{2} + x \cdot 4 - 5 (5 x) - 5 \cdot 4 - 5 x^{2}$

Move $4$ to the left of $x$ .

$y = 5 x^{2} + 4 \cdot x - 5 (5 x) - 5 \cdot 4 - 5 x^{2}$

Multiply $5$ by $- 5$ .

$y = 5 x^{2} + 4 x - 25 x - 5 \cdot 4 - 5 x^{2}$

Multiply $- 5$ by $4$ .

$y = 5 x^{2} + 4 x - 25 x - 20 - 5 x^{2}$

Subtract $25 x$ from $4 x$ .

$y = 5 x^{2} - 21 x - 20 - 5 x^{2}$

Combine the opposite terms in $5 x^{2} - 21 x - 20 - 5 x^{2}$ .

Subtract $5 x^{2}$ from $5 x^{2}$ .

$y = - 21 x - 20 + 0$

Add $- 21 x - 20$ and $0$ .

$y = - 21 x - 20$

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.

$- 21 x \to 1$

$- 20 \to 0$

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.

$- 21 x$

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.

$- 21 x$

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

$- 21$

Step 5

List the results.

Polynomial Degree: $1$

Leading Term: $- 21 x$

Leading Coefficient: $- 21$

Find the Degree, Leading Term, and Leading Coefficient y=(x-5)(5x+4)-5x^2

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