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 $4x^3y^2 - 7x^2y^4 + 5$?

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

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: $(x + 2)(x^2 - x + 3)$.

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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