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
No, the student is incorrect.
First, let's count the number of terms in the expression: −4x^5 − 3x^4 + 8x^7 − 6x has a total of four terms. So, the student is correct about the number of terms.
Next, let's determine the degree of the expression. The degree of an expression is the highest power of x among all its terms. In this case, the highest power of x is 7, so the degree of the expression is 7. Therefore, the student is incorrect about the degree of 4.
Lastly, let's consider the leading coefficient. The leading coefficient is the coefficient of the term with the highest power of x. In this case, the term with the highest power of x is 8x^7. The coefficient of this term is 8, which is positive. Therefore, the student is incorrect in stating that the leading coefficient is negative.
In summary, the student is incorrect about the degree and leading coefficient, but correct about the number of terms. The correct information is that the expression has four terms, a degree of 7, and a positive leading coefficient.