A student states that −4x^5−3x^4+8x^7−6x
has four terms, a degree of 4, and a negative leading coefficient.
Is the student correct? Explain
(3 points)
No, the student is not correct.
The given expression, −4x^5−3x^4+8x^7−6x, actually has five terms: -4x^5, -3x^4, 8x^7, -6x.
The degree of a term is determined by the exponent of the variable. In this case, the term with the highest degree is 8x^7, which has a degree of 7. Therefore, the degree of the expression is 7, not 4.
Additionally, the leading coefficient is the coefficient of the term with the highest degree. In this case, the leading coefficient is 8, which is positive, not negative.