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
No, the student is not correct.
The given expression can be rewritten as -4x^5 + (-3x^4) + 8x^7 + (-6x).
To determine the number of terms, we count the individual parts of the expression that are added or subtracted. In this case, we have 4 terms: -4x^5, -3x^4, 8x^7, and -6x.
The degree of the expression is determined by the highest exponent of x. In this case, the highest exponent is 7, so the degree of the expression is 7.
The leading coefficient is the coefficient of the term with the highest degree. In this case, the term with the highest degree is 8x^7, and the coefficient is 8. Since the coefficient is positive, the student's statement that the leading coefficient is negative is incorrect.
Therefore, the student is incorrect in all three statements.