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?

Accepted Answer

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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