List the terms, coefficients, and degree of the following polynomial: 7x^4 – 3x^2 + 5x + 2/3
Can someone help me with this please.
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Here is an example to help you.
3x^3 - 7x^2 + x - 4
Terms: .........3x^3....-7x^2....x....-4
Coefficients: ...3...........-7......1....-4
Degree (greatest exponent): 3
Thank you
Sure! I can help you with that.
A polynomial is an expression that consists of one or more terms, where each term is a constant multiplied by one or more variables raised to nonnegative integer powers.
Let's break down the given polynomial: 7x^4 – 3x^2 + 5x + 2/3
Terms: A polynomial is made up of multiple terms, separated by addition or subtraction. In this case, the polynomial has four terms - 7x^4, -3x^2, 5x, and 2/3.
Coefficients: The coefficient of a term is the numerical factor that precedes the variable. In this polynomial, the coefficients are 7, -3, 5, and 2/3.
Degree: The degree of a term is the exponent of the variable. For example, the term 7x^4 has a degree of 4, the term -3x^2 has a degree of 2, the term 5x has a degree of 1, and the term 2/3 has a degree of 0 (a constant term).
The degree of the entire polynomial is the highest degree among its terms. In this case, the term with the highest degree is 7x^4, so the degree of the polynomial is 4.
So, to summarize, the polynomial 7x^4 – 3x^2 + 5x + 2/3 has four terms, with coefficients 7, -3, 5, and 2/3, and a degree of 4.