Answers:
- Degree = 6
- Leading term = 5ab^5
- Leading coefficient = 5
- Constant term = 8
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Explanation:
When we have multivariable terms like this, we add up the exponents for each monomial separately.
- The first term -2a^3b^2 has its exponents add to 3+2 = 5
- The second term 5ab^5, aka 5a^1b^5, has the exponents add to 1+5 = 6
- The third term can be thought of as 7a^0b^4, so its exponents add to 0+4 = 4
- The last term 8 is really 8a^0b^0, and its exponent sum is 0
The degree of this entire multivariable polynomial is the largest sum calculated in the list above. That sum being 6. Therefore, the degree of the polynomial is 6.
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From that we can circle the leading term 5ab^5 since the leading term is always the one with the largest exponent sum (aka degree). The current polynomial as written is not standard form. It should be this:
5ab^5 - 2a^3b^2 + 7b^4 + 8
Notice how the exponent sums decrease when going from left to right. The largest sum is always listed first. Hence the "leading" aspect of "leading term".
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The leading coefficient is the coefficient of the leading term.
The coefficient of 5ab^5 is 5. More specifically, it's the first "5" mentioned. As another example, the coefficient of 7ab^5 would be 7.
The leading coefficient is 5
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The constant is the term without any variables attached to it. It stays the same number the entire time.
The constant term is 8
