A circle and a line intersect at most twice. A circle and aparabola intersect at most four times. Deduce that a circleand the graph of a polynomial of degree 3 intersect at mostsix times. What do you conjecture about a polynomial ofdegree 4? What about a polynomial of degree n? Can youexplain your conclusions using an algebraic argument?

The image shows the graph of a degree 7 polynomial with leading coefficient -1 whose roots are -1, 0.5, 2.25, 4, Answer the following statementsa. What is the multiplicity of the first root?b. What is the multiplicity of the second root?c. Find the multiplicity of the third rootd.Find the multiplicity of the last roote. Find the value of the constant term Answer

Create a polynomial, in standard form, of at degree 5 or higher. It must have at least one imaginary zero. List all possible Rational Zeros Find all zeros and write in standard form. Identify all multiplicities and explain how they affect the graph.   Find all intercepts Explain how you would find the end behavior for any polynomial then identify the end behavior for this polynomial.

What is the maximum number of real roots a 5th-degree polynomial can have?