Introduction To Polynomials Assignment

Classify the polynomial and determine its degree. The polynomial -2x2 - x + 2 is a _______ with a degree of _______.

Trinomial 2

Raj was asked to fully simplify this polynomial and put it into standard form. 2x2y + 8x3 - xy2 - 2x3 + 3xy2 + 6y3 Raj simplified the polynomial with a final term of 6y3. What is the first term of the polynomial Raj ended up with? 6x3 8x3 2xy2 3xy2

A.) 6x3

For the expression 5x^?y^3 + xy^2 + 8 to be a trinomial with a degree of 5, the missing exponent on the x-term must be _______.

2

Which algebraic expressions are polynomials? Check all that apply. 2x^3 - 1/x x^3y - 3x^2 + 6x y^2 + 5y - sqrt3 2 - sqrt4x -xsqrt6 -1/3x^3 - 1/2x^2 + 1/4

2 3 5 6

Which polynomial represents the algebra tile configuration shown? x^2 + 3x + 4 x^2 + 3x − 4x −x^2 − 7 −x^2 + 3x − 4

D.) −x^2 + 3x − 4

Which terms could be used as the first term of the expression below to create a polynomial with a degree of 5 written in standard form? Check all that apply. ___ + 2x2y2 - 3xy3 -4x3y2 x3 8.4x4y2 5x4y -xy3 -2x4/y

1 4

Which algebraic expressions are binomials? Check all that apply. xysqrt8 x2^y - 3x 6y^2 - y y^2 + sqrty 4xy - 2/5 x^2 + 3/x

2 3 5

Which algebraic expression is a polynomial with a degree of 3? 4x^3 - 2/x 2y^3 + 5y^2 - 5y 3y^3 - sqrt4y -xysqrt6

B.) 2y^3 + 5y^2 - 5y

Which represents the polynomial below written in standard form? x^2/2 - 3x + 4x^3 + 6 6 + x^2/2 - 3x + 4x^3 4x^3 + x^2/2 - 3x + 6 -3x + 4x^3 + 6 + x^2/2 x^2/2 + 4x^3 - 3x + 6

B.) 4x^3 + x^2/2 - 3x + 6

Which polynomial correctly combines the like terms and puts the given polynomial in standard form? -5x3y3 + 8x4y2 - xy5 - 2x2y4 + 8x6 + 3x2y4 - 6xy5 -7xy5 + 5x2y4 - 5x3y3 + 8x4y2 + 8x6 5xy5 + 8x4y2 + x2y4 - 5x3y3 + 8x6 8x6 + 5xy5 + 8x4y2 + x2y4 - 5x3y3 8x6 + 8x4y2 - 5x3y3 + x2y4 - 7xy5

D.) 8x6 + 8x4y2 - 5x3y3 + x2y4 - 7xy5

Marcus states that the polynomial expression 3x3 - 4x2y + y3 + 2 is in standard form. Ariel states that it should be y3 - 4x2y + 3x3 +2. Explain which student is correct and why.

They are both correct because there is more than one way to write a multivariable polynomial in standard form. Marcus has the exponents on the x variable in descending order from the highest degree to the lowest degree. Ariel has the exponents on the y variable in descending order from the highest degree to the lowest degree.