The degree of a polynomial is the highest power of the variable. In the polynomial 3x² - 4x + 5, we identify the highest exponent among all terms. The terms have powers 2, 1, and 0 respectively, so the highest power is 2. Choice A might confuse the leading coefficient (3) with the degree.

We need to expand (x - 1)² using the perfect square formula (a - b)² = a² - 2ab + b². Here, a = x and b = 1, so (x - 1)² = x² - 2(x)(1) + 1² = x² - 2x + 1. Choice C would result from incorrectly applying the formula as (x + 1)² instead.

The leading coefficient is the coefficient of the term with the highest degree. In the polynomial -x³ + 4x² - x, the highest degree term is -x³ with degree 3. Since -x³ = (-1)x³, the coefficient of this term is -1, which is the leading coefficient. Choice C might incorrectly identify the coefficient of the x² term.

The degree of a polynomial is the highest power of the variable. In the polynomial -3x² + 6x, we identify the highest exponent among all terms. The terms have powers 2 and 1 respectively, so the highest power is 2. Choice C might confuse the leading coefficient (-3) with the degree.

The polynomial x² - 4 is a difference of squares pattern: a² - b² = (a - b)(a + b). Here, x² - 4 = x² - 2², so a = x and b = 2. Therefore, x² - 4 = (x - 2)(x + 2). Choice C would incorrectly use 3 instead of 2 as the square root of 4.

We need to identify the leading coefficient of -2x³ + 4x² - x. The leading coefficient is the coefficient of the term with the highest degree. The highest degree term is -2x³, which has degree 3. The coefficient of this term is -2, so the leading coefficient is -2.

The leading coefficient is the coefficient of the term with the highest degree. In the polynomial -5x² + 3x + 4, the highest degree term is -5x² with degree 2. The coefficient of this term is -5, which is the leading coefficient. Choice B might incorrectly identify the coefficient of the linear term instead.

The leading coefficient is the coefficient of the term with the highest degree. In the polynomial 7x³ + 5x² - 4x + 6, the highest degree term is 7x³ with degree 3. The coefficient of this term is 7, which is the leading coefficient. Choice B might incorrectly identify the coefficient of the x² term instead.

The degree of a polynomial is the highest exponent of the variable. In w(x) = 3x² + 0x + 4, the terms have exponents: 3x² has exponent 2, 0x has exponent 1, and 4 has exponent 0. The highest exponent is 2, so the degree is 2. Choice A might confuse the constant term with the degree.

We need to simplify x(x - 1) + 2(x + 1) by distributing and combining like terms. First distribute: x(x - 1) = x² - x and 2(x + 1) = 2x + 2. Combine: x² - x + 2x + 2 = x² + (-x + 2x) + 2 = x² + x + 2. Choice B would result from sign errors when combining the x terms.