Video Transcript
Determine the coefficient and degree of negative seven ๐ฅ cubed.
For a term with one variable, in this case negative seven ๐ฅ cubed, the degree is the variableโs exponent or power. Therefore, in this case, the degree of negative seven ๐ฅ cubed is three.
The coefficient of a term is the number that is multiplied by that term. In this case, the coefficient of negative seven ๐ฅ cubed is negative seven, as this negative seven is multiplied by the ๐ฅ cubed.
Therefore, the degree is equal to three. And the coefficient is equal to negative seven.
This process can be extended to look at not just individual terms, but also polynomials. In terms of polynomials, we need to initially look for the leading term. This is the term with the highest power or exponent. And its coefficient is called the leading coefficient.
This can be demonstrated by looking at the example: four ๐ฅ to the power of five plus seven ๐ฅ squared minus nine ๐ฅ plus four. The leading term in this polynomial is four ๐ฅ to the power of five, as this is the term with the highest power or exponent. Looking at the term four ๐ฅ to the power of five, we can see that its degree is five and its coefficient is four. Therefore, the degree of the polynomial four ๐ฅ to the power five plus seven ๐ฅ squared minus nine ๐ฅ plus four is equal to five. And its leading coefficient is four.
