Algebra 2 | Unit 2 | Lesson 4: Combining Polynomials | Practice Problems

Here are two expressions whose product is a new expression, $$A$$ . $$(5x^4 + \boxed{\phantom{33}}x^3)(4x^{\boxed{\phantom{3}}} - 6) = A$$ Andre says that any real number can go in either of the boxes and $$A$$ will be a polynomial. Is he correct? Explain your reasoning.

Lin divides the polynomial $$2x^2 - 4x + 1$$ by 4 and gets $$0.5x^2 - x + 0.25$$ . Is $$0.5x^2 - x + 0.25$$ a polynomial? Explain your thinking.

What is the result when any 2 integers are multiplied?

Clare wants to make an open-top box by cutting out corners of a 30 inch by 25 inch piece of poster board and then folding up the sides. The volume $$V(x)$$ in cubic inches of the open-top box is a function of the side length $$x$$ in inches of the square cutouts. Write an expression for $$V(x)$$ .

What is a reasonable domain for $$V$$ in this context?

(a)  

Identify the degree, leading coefficient, and constant value of each of the following polynomials.
$$f(x)=2x^5 - 8 x^2 - x - 6$$
$$h(x)=x^3 - 7 x^2 - x + 2$$
$$g(x)=5 x^2-4 x^3 + 2x +5.4$$

Which point is a relative minimum?