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.

Accepted Answer

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.

Accepted Answer

Question 17

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

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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