Exploring Operations with Polynomials

What is the degree of the polynomial x^4 + 3x^2 - 2?

• 2

• 5

• 3

• 4

When subtracting polynomials, what should you do with the signs of the terms in the polynomial being subtracted?

• Ignore them

• Change them to negative

• Change them to positive

• Keep them the same

What is the result of combining like terms in the expression 3x^2 - x^2 + 2x + 2x - 7 - 10?

• 3x^2 + 4x - 17

• 2x^2 + 2x - 17

• 4x^2 + 4x - 17

• 2x^2 + 4x - 17

What common mistake do people make when cubing a binomial like 2x - y?

• Ignoring the negative sign

• Multiplying the coefficients directly

• Adding the exponents

• Distributing the cube to each term

What is the correct first step in multiplying the binomials 2x - y and 2x - y?

• Square each term

• Multiply each term in the first binomial by each term in the second binomial

• Combine like terms

• Add the terms

What is the result of multiplying 2x and 4x^2 in the expression (2x - y)(2x - y)?

• 4x^2

• 8x^3

• 6x^2

• 8x^2

What is the result of multiplying -y and 4x^2 in the expression (2x - y)(2x - y)?

• 4x^2y

• -4x^2y

• -4xy

• 4xy

What is the final result of multiplying the binomials (2x - y)(2x - y)(2x - y)?

• 8x^3 - 12x^2y + 6xy^2 - y^3

• 8x^3 - 8x^2y + 4xy^2 - y^3

• 8x^3 - 12x^2y + 4xy^2 - y^3

• 8x^3 - 8x^2y + 6xy^2 - y^3

Why is it important to write out and distribute terms when multiplying binomials?

• To impress the teacher

• To make it look neat

• To avoid mistakes

• To save paper

What is a good practice to minimize mistakes when working on polynomial problems?

• Write small to save paper

• Use a calculator for every step

• Write large and spread out on the page

• Skip steps to save time