Question 1

Which of the following expressions is a polynomial in standard form?

Accepted Answer

$$3x^2 + 2x - 5$

Question 2

What is the degree of the polynomial $$4x^3y^2$ - 7x^2$y^4 + 5$?

Accepted Answer

$$7$$

Question 3

Which term is the leading coefficient in the polynomial $$-8x^5$$ + $$3x^3 - x + 7$?

Accepted Answer

$$-8$$

Question 4

Simplify the sum: $$(2x^2 + 5x - 3$$) + $$(4x^2 - 2x + 7$$)$$.

Accepted Answer

$$6x^2 + 3x + 4$

Question 5

Subtract the polynomials: $$(5x^3$$ - $$2x^2 + 4x - 1$$) - $$(3x^3$$ + $$x^2 - 2x + 6$$)$$.

Accepted Answer

$$2x^3$$ - $$3x^2 + 2x - 7$

Question 6

Multiply the monomials: $$(-3x^2y)(4x^3$y^2$$)$$.

Accepted Answer

$$-12x^5y^3$

Question 7

Use the distributive property to multiply: $$2x(x^2 + 3x - 4$$)$$.

Accepted Answer

$$2x^3$$ + $$6x^2 - 8x$

Question 8

Multiply the binomial and trinomial: $$(x + 2)(x^2$ - x + 3).$$

Accepted Answer

Question 9

Apply the FOIL method to multiply $$(2x - 5)(x + 3).$$

Accepted Answer

$$2x^2 + x - 15$

Question 10

Which formula represents the product of the sum and difference of two terms, $$A$$ and $$B$$?

Accepted Answer

$$(A + B)(A - B) = A^2$ - B^2$

Question 11

Find the square of the binomial $$(3x - 4).$$

Accepted Answer

$$9x^2 - 24x + 16$

Question 12

A polynomial in two variables, $$x$$ and $$y$$, has the term $$7x^2y^3$. What is the degree of this term?

Accepted Answer

$$5$$

Question 13

Subtract the polynomials in two variables: $$(4x^2y$$ + $$3xy^2$$ - $$2y^2$$) - $$(2x^2y$$ - $$xy^2$$ + $$y^2$$)$$.

Accepted Answer

$$2x^2y$$ + $$4xy^2$$ - $$3y^2$$

Question 14

Multiply the polynomials in two variables: $$(2x + 3y)(x - y).$$

Accepted Answer

$$2x^2 + x y$$ - $$3y^2$$

Question 15

Which of the following is NOT a polynomial?

Accepted Answer

$$x^2$$ + \frac{1}{x}$$

Question 16

A chemist is modeling the concentration of a solution over time using the polynomial $$C(t) = 4t^3$ - 2t^2$ + 7. $$What is the constant term in this polynomial?

Accepted Answer

$$7$$

Question 17

If $$f(x) = x^2$ - 3x + 2$$ and $$g(x) = 2x^2$ + x - 5$$, what is $$f(x) + g(x)$$?

Accepted Answer

$$3x^2 - 2x - 3$

Question 18

A medical researcher uses the polynomial $$P(x) = 5x^4$ - 2x^3$ + x^2$ to model the growth of bacteria. What is the degree of this polynomial?

Accepted Answer

$$4$$

Question 19

Which operation is used to combine like terms in polynomials?

Accepted Answer

Addition and subtraction

Polynomials: Fundamental Concepts and Operations (College Algebra Study Notes)

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