Answer the questions about the following polynomial.
one half, plus, 5, x, to the power 4 , minus, 7, x, plus, x, squared
The polynomial is: 1/2 + 5x^4 - 7x + x^2
Now let's answer the questions:
1. What is the degree of the polynomial?
The degree of the polynomial is the highest power of x. In this case, the highest power of x is 4, so the degree of the polynomial is 4.
2. What is the coefficient of the x^2 term?
The coefficient of the x^2 term is the number multiplied by x^2. In this case, the coefficient of the x^2 term is 1.
3. What is the constant term?
The constant term is the number without any variable attached. In this case, the constant term is 1/2.
4. Is the polynomial in standard form?
Yes, the polynomial is in standard form. Standard form means that the terms are arranged in descending order of powers of x, so the polynomial is written correctly.
5. Is the polynomial a monomial, binomial, trinomial, or polynomial with more than three terms?
The polynomial is a polynomial with more than three terms. It has four terms: 1/2, 5x^4, -7x, and x^2.
6. Can the polynomial be factored?
Yes, the polynomial can be factored, but it may not factor easily. Factoring involves finding the common factors and grouping terms with common factors together. In this case, the polynomial may require more complex factoring methods such as factoring by grouping or factoring using the quadratic formula.