Match each sequence with one of the recursive definitions. Note that only the part of the definition showing the relationship between the current term and the previous term is given so as not to give away the solutions. One of the sequences matches two recursive definitions.

Han is multiplying \(10x^4\) by \(0.5x^3\) and gets \(5x^7\). He says that \(0.5x^3\) is not a polynomial because 0.5 is not an integer. What is the error in Han’s thinking? Explain your reasoning.

Here are two expressions whose sum is a new expression, \(A\).

\(\displaystyle (2x^2 + 5)+(6x^{\boxed{\phantom{33}}} -7) = A\)

Select all the values that we can put in the box so that \(A\) is a polynomial.

Match each quadratic expression given in factored form with an equivalent expression in standard form. One expression in standard form has no match.