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

What is the sum of $(8p^2 - 2p + 15)$ and $(11 - 2p^2 - 1)$ in standard form?

Question 4

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

Accepted Answer

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

Question 5

Find the result of $(4x^2 + 5x) - (7x + 3x^2 + 1)$ in standard form.

Accepted Answer

$x^2 - 2x - 1$

Question 6

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

Accepted Answer

$2x^2 + 2x + 2$

Question 7

Which of the following is a cubic binomial?

Accepted Answer

$x^3 - 8$

Question 8

Subtract $(2w^2 - 5w + 10)$ from $(w^3 + 6w^2 - 2)$ and write the result in standard form.

Accepted Answer

$w^3 + 4w^2 + 5w - 12$

Question 9

A company models its profit with $P(x) = 2x^2 + 3x - 5$ and its expenses with $E(x) = x^2 - 4x + 7$. What is the net profit polynomial $N(x) = P(x) - E(x)$ in standard form?

Accepted Answer

$x^2 + 7x - 12$

Question 10

Which of the following is NOT a polynomial?

Accepted Answer

$4x^{-2} + 3x$

Question 11

Find the sum: $(3a^2 - a + 3) + (4a^2 - 5)$ in standard form.

Accepted Answer

$7a^2 - a - 2$

Question 12

A medical researcher models the growth of bacteria with $B_1(t) = 5t^2 + 3t$ and $B_2(t) = 2t^2 - 4t + 7$. What is the total bacteria growth polynomial?

Accepted Answer

$7t^2 - t + 7$

Question 13

Classify the polynomial $2x^4 - x^3 + 5x^2 + x - 7$ by degree and number of terms.

Accepted Answer

Quartic polynomial with 5 terms

Question 14

Find the result of $(2x^2 + 3y^2 - z^2) - (x^2 - y^2 - z^2) + (4x^2 - 3y^2)$ in standard form.

Accepted Answer

$5x^2 + 4y^2$

Question 15

Which of the following is the correct classification for the polynomial $10x$?

Accepted Answer

Linear monomial

Question 16

Write $y^2 + 3y^4 - 7y + 2y^3 - 4$ in standard form.

Accepted Answer

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

Question 17

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 18

Which of the following is a quadratic binomial?

Accepted Answer

$7x^2 - 1$

Question 19

Find the sum: $(2x^2 - 6x - 2) + (x^2 + 4x)$ in standard form.

Accepted Answer

$3x^2 - 2x - 2$

Question 20

A population model is given by $P_1(t) = 4t^3 - 2t^2 + t$ and $P_2(t) = -t^3 + 5t^2 - 3t$. What is the sum $P_1(t) + P_2(t)$ in standard form?

Accepted Answer

$3t^3 + 3t^2 - 2t$

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

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