Question 1

Which of the following is the correct result when adding the polynomials $$(4x^2 - 3x + 7) + (2x^2 + 5x - 4)$$?

Accepted Answer

$$6x^2 + 2x + 3$

Question 2

Subtract the polynomial $$(3x^3 - 2x^2 + 4x - 5)$$ from $$(5x^3 + x^2 - 2x + 7). $$What is the result?

Accepted Answer

$$2x^3$$ + $$3x^2 - 6x + 12$

Question 3

A chemist is mixing two solutions. The concentration of a chemical in the first solution is modeled by $$2x^2 + 3x - 1$, and in the second by -x^2$ + 4x + 5. $$What is the total concentration after mixing?

Accepted Answer

$$x^2 + 7x + 4$

Question 4

Which of the following is the opposite of the polynomial $$4x^2 - 7x + 9$$?

Accepted Answer

$$-4x^2 + 7x - 9$

Question 5

A company’s profit in year 1 is modeled by $$3x^2 - 2x + 5$, and in year 2 by -x^2$ + 4x - 3. $$What is the change in profit from year 1 to year 2 (year 2 minus year 1)?

Accepted Answer

$$-4x^2 + 6x - 8$

Question 6

Simplify the expression $$(-2x^3 + 5x^2 - 4x + 6) + (3x^3 - 2x^2 + x - 8).$$

Accepted Answer

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

Question 7

If you subtract $$(x^2 - 3x + 2)$$ from $$(4x^2 + x - 5)$$, what is the resulting polynomial?

Accepted Answer

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

Question 8

A biologist models the population of two species as $$P_1$$ = $$6x^2 - 2x + 8$ and P_2$ = -4x^2$ + 5x - 3. $$What is the combined population model?

Accepted Answer

$$2x^2 + 3x + 5$

Question 9

Which of the following is the result of subtracting $$(2x^2 - 5x + 4)$$ from $$(x^2 + 3x - 7)$$?

Accepted Answer

$$-x^2 + 8x - 11$

Question 10

A physics experiment models the velocity of two objects as $$v_1$$ = $$5x^2 - 3x + 2$ and v_2$ = -2x^2$ + 4x - 6. $$What is the sum of their velocities?

Accepted Answer

$$3x^2 + x - 4$

Question 11

Simplify the expression $$[2x^3 - 4x^2 + 5x - 1] - [x^3 + 2x^2 - 3x + 6].$$

Accepted Answer

$$x^3$$ - $$6x^2 + 8x - 7$

Question 12

Which of the following is the correct result when adding $$(7x^2 - 2x + 3)$$ and $$(-4x^2 + 5x - 8)$$?

Accepted Answer

$$3x^2 + 3x - 5$

Question 13

A medical researcher models the growth of two bacteria cultures as $$B_1$$ = $$4x^2 + 2x - 1$ and B_2$ = 3x^2$ - 5x + 6. $$What is the difference $$B_1$$ - $$B_2$$?

Accepted Answer

$$x^2 + 7x - 7$

Question 14

Simplify the following: $$[5x^3 - 2x^2 + 7x - 4] + [-3x^3 + 6x^2 - 2x + 9].$$

Accepted Answer

$$2x^3$$ + $$4x^2 + 5x + 5$

Question 15

If you subtract $$(4x^2 - 3x + 2)$$ from $$(2x^2 + 5x - 7)$$, what is the result?

Accepted Answer

$$-2x^2 + 8x - 9$

Question 16

A business’s revenue is modeled by $$R = 8x^2$ - 3x + 10$$ and its expenses by $$E = 5x^2$ + 2x - 4. $$What is the net profit $$R - E$$?

Accepted Answer

$$3x^2 - 5x + 14$

Question 17

Which of the following is the result of adding $$(x^3 - 2x^2 + 4x - 1)$$ and $$(2x^3 + 5x^2 - 3x + 6)$$?

Accepted Answer

$$3x^3$$ + $$3x^2 + x + 5$

Question 18

A city’s population growth is modeled by $$P_1$$ = $$2x^2 + 3x - 5$ in the first decade and P_2$ = 4x^2$ - 2x + 7 in $$the second. What is the total growth over both decades?

Accepted Answer

$$6x^2 + x + 2$

Adding and Subtracting Polynomials: Integrated Review

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