Adding and Subtracting Polynomials

Adding which terms to 3x2y would result in a monomial? Check all that apply. 3xy -12x2y 2x2y2 7xy2 -10x2 4x2y 3x3

-12x^2y 4x^2y

Find: (4x2y3 + 2xy2 - 2y) - (-7x2y3 + 6xy2 - 2y) Place the correct coefficients in the difference. ? x^2y^3 + ? xy^2 + ? y

1. 11 2. -4 3. 0

A family needs to build fencing around their rectangular home and square swimming pool, depicted below. The total amount of fencing they need can be written as ? x + 10. If x = 5; The family needs ? yards of fencing for their home. The family needs ? yards of fencing for their pool.

1. 38 2. 160 3. 40

Lorne subtracted 6x3 - 2x + 3 from -3x3 + 5x2 + 4x - 7. Use the drop-down menus to identify the steps Lorne used to find the difference. 1. (-3x3 + 5x2 + 4x - 7) + (-6x3 + 2x - 3) 2. (-3x3) + 5x2 + 4x + (-7) + (-6x3) + 2x + (-3) 3. [(-3x3) + (-6x3)] + [4x + 2x] + [(-7) + (-3)] + [5x2] 4. -9x3 + 6x + (-10) + 5x2 5. -9x3 + 5x2 + 6x - 10

1. Wrote as addition of the additive inverse 2. Wrote terms as addition of opposite 3. Grouped like terms 4. Combined like terms

The sum of two polynomials is 10a2b2 - 8a2b + 6ab2 - 4ab + 2. If one addend is -5a2b2 + 12a2b - 5, what is the other addend? 1. 15a2b2 - 20a2b + 6ab2 - 4ab + 7 2. 5a2b2 - 20a2b2 + 7 3. 5a2b2 + 4a2b2 + 6ab - 4ab - 3 4. -15a2b2 + 20a2b2 - 6ab + 4ab - 7

A. 15a2b2 - 20a2b + 6ab2 - 4ab + 7

Which property does each equation demonstrate? x2 + 2x = 2x + x2 associative property, closure property, commutative property (3z4 + 2z3) - (2z4 + z3) = z4 + z3 associative property, closure property, commutative property (2x2 + 7x) + (2y2 + 6y) = (2y2 + 6y) + (2x2 + 7x) associative property, closure property, commutative property

Commutative Property Closure Property Commutative Property

What is the sum of the given polynomials in standard form? (x2 - 3x) + (-2x2 + 5x - 3) -3x^2 + 8x - 3 -x^2 - 2x - 3 3x^2 - 8x + 3 -x^2 + 2x - 3

D. -x^2+2x-3

The revenue, in dollars, of a company that produces video game systems can be modeled by the expression 5x2 + 2x - 80. The cost, in dollars, of producing the video game systems can be modeled by 5x2 - x + 100, where x is the number of video game systems sold. If profit is the difference between the revenue and the cost, what expression represents the profit? Profit can be modeled by the polynomial expression ? If 1,000 video game systems are sold, the company's profit is ?

1. 3x - 180 2. $ 2,820

Which polynomials are listed with their correct additive inverse? Check all that apply. x2 + 3x - 2; -x2 - 3x + 2 -y7 - 10; -y7 + 10 6z5 + 6z5 - 6z4; (-6z5) + (-6z5) + 6z4 x - 1; 1 - x (-5x2) + (-2x) + (-10); 5x2 - 2x + 10

A. x^2+3x-2; -x^2-3x+2 C. 6z^5+6z^5-6z^4; (-6z^5)+(-6z^5)+6z^4

Cory writes the polynomial x7 + 3x5 + 3x + 1. Melissa writes the polynomial x7 + 5x + 10. Is there a difference between the degree of the sum and the degree of the difference of the polynomials? A. Adding their polynomials together or subtracting one polynomial from the other both result in a polynomial with degree 7. B. Adding their polynomials together or subtracting one polynomial from the other both result in a polynomial with degree 5. C. Adding their polynomials together results in a polynomial with degree 14, but subtracting one polynomial from the other results in a polynomial with degree 5. D. Adding their polynomials together results in a polynomial with degree 7, but subtracting one polynomial from the other results in a polynomial with degree 5.

D