Video: Determining the Degree and Coefficient of an Algebraic Term

Determine the coefficient and degree of βˆ’7π‘₯Β³.

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Video Transcript

Determine the coefficient and degree of negative seven π‘₯ cubed.

For a term with one variable, in this case negative seven π‘₯ cubed, the degree is the variable’s exponent or power. Therefore, in this case, the degree of negative seven π‘₯ 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 π‘₯ cubed is negative seven, as this negative seven is multiplied by the π‘₯ 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 π‘₯ to the power of five plus seven π‘₯ squared minus nine π‘₯ plus four. The leading term in this polynomial is four π‘₯ to the power of five, as this is the term with the highest power or exponent. Looking at the term four π‘₯ 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 π‘₯ to the power five plus seven π‘₯ squared minus nine π‘₯ plus four is equal to five. And its leading coefficient is four.

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