A student states that −4x5−3x4+8x7−6x
has four terms, a degree of 4, and a negative leading coefficient.
Is the student correct? Explain
(3 points)
The student is not correct. To determine the number of terms, we count the number of different variables or variable combinations. In the expression −4x^5−3x^4+8x^7−6x, there are only three different variables or variable combinations: x^5, x^4, and x^7. Therefore, the expression has three terms, not four.
The degree of an expression is determined by the highest exponent of the variable. In this case, the highest exponent is 7 in the term 8x^7. Therefore, the degree of the expression is 7, not 4.
Lastly, 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.
Therefore, the student is not correct in all three statements.