Answers:
- Standard Form: 5x^2 - x + 4
- Leading coefficient: 5
- Constant: 4
- Degree: 2
- Number of terms: 3
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Explanation:
The term with the largest exponent will go first, followed by the next largest exponent, and so on. This will get the polynomial into standard form. So 4+5x^2-x turns into 5x^2-x+4. You can think of this as 5x^2-x^1+4x^0. Note the exponents counting down: 2,1,0.
Each term is separated by a plus or a minus. We can think of 5x^2-x+4 as 5x^2+(-x)+4
The leading term is the first term 5x^2. It has the coefficient of 5, so the leading coefficient of the overall polynomial is 5.
The constant is the term without any variables attached to it. So the constant is 4. As the name implies, the constant doesn't change no matter what x changes to. In contrast, the 5x^2 term does change as x changes.
The degree is the largest exponent, so in this case it would be 2. After you get the polynomial into standard form, it's the first exponent on the left.
As mentioned earlier, each term is separated by a plus or a minus. So we have three terms here. We consider this a trinomial since "tri" means "three". More specifically, this is a quadratic trinomial. Any quadratic will have the largest exponent being 2.
