Question 1

Which of the following is the correct standard form of the polynomial $2x + 3 + x^2$?

Accepted Answer

$x^2 + 2x + 3$

Question 2

Classify the polynomial $-7x^2 + 4x - 1$ by its degree and number of terms.

Accepted Answer

Quadratic trinomial

Question 3

Which of the following is the sum of $(3x^2 - 4x + 5)$ and $(2x^2 + 7x - 3)$, written in standard form?

Accepted Answer

$5x^2 + 3x + 2$

Question 4

A chemist is mixing two solutions. The concentration of chemical $A$ is modeled by $C_1(x) = 4x^2 - 3x + 2$ and $C_2(x) = -2x^2 + 5x - 1$. What is the combined concentration, in standard form?

Accepted Answer

$2x^2 + 2x + 1$

Question 5

Write the polynomial $9x^4 - 2x^2 + 7x - 8x^3 + x^5 - 4$ in standard form.

Accepted Answer

$x^5 + 9x^4 - 8x^3 - 2x^2 + 7x - 4$

Question 6

Subtract $(3 - 9m^2 - 2m)$ from $(2m - 3 + 7m^2)$ and write the result in standard form.

Question 7

A company models its profit for two products as $P_1(x) = 5x^3 - 2x^2 + 4x$ and $P_2(x) = -3x^3 + x^2 - 6x$. What is the total profit function, in standard form?

Accepted Answer

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

Question 8

Which of the following is a cubic binomial?

Accepted Answer

$x^3 - 8$

Question 9

Find the sum of $(2x^2 - 6x - 2)$ and $(x^2 + 4x)$, and classify the result.

Accepted Answer

$3x^2 - 2x - 2$, quadratic trinomial

Question 10

Which of the following is the correct classification for the polynomial $2x^4 - x^3 + 5x^2 + x - 7$?

Accepted Answer

Quartic polynomial with 5 terms

Question 11

A medical researcher models the growth of bacteria with $B_1(t) = 8t^2 - 3t + 5$ and $B_2(t) = -2t^2 + 7t - 1$. What is the total bacteria growth model, in standard form?

Accepted Answer

$6t^2 + 4t + 4$

Question 12

Subtract $(-a^2 - 5ab + 3b^2)$ from $(3a^2 - 2ab + 3b^2)$ and write the result in standard form.

Accepted Answer

$4a^2 + 3ab$

Question 13

Which of the following is the standard form of $y^2 + 3y^4 - 7y + 2y^3 - 4$?

Accepted Answer

$3y^4 + 2y^3 + y^2 - 7y - 4$

Question 14

A business's revenue is modeled by $R(x) = 4x^2 + 5x + 10$ and its expenses by $E(x) = 2x^2 + 3x + 7$. What is the profit function $P(x) = R(x) - E(x)$?

Accepted Answer

$2x^2 + 2x + 3$

Question 15

Which of the following is a quadratic binomial?

Accepted Answer

$x^2 - 8$

Question 16

Find the sum of $(8p^2 - 2p + 15)$ and $(11 - 2p^2 - 1)$, and write the result in standard form.

Question 17

Which of the following is the degree of the polynomial $-3m^2n^2 + 8mn^3 + m^3n$?

Accepted Answer

4

Question 18

A population model is given by $P(t) = 2t^3 - 5t^2 + 4t - 7$. What is the degree and number of terms of this polynomial?

Accepted Answer

Degree 3, 4 terms

Question 19

Which of the following is the correct standard form of $-2b^2 + 5ab + 7a^2$?

Accepted Answer

$7a^2 + 5ab - 2b^2$

College Algebra Study Guide: Polynomials – Standard Form, Classification, Addition & Subtraction

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