Polynomial Review Warmup

Classify by number of terms:
2x – 9

• Monomial

• Binomial

• Trinomial

• 4-Term Polynomial

Answer explanation

The given expression has two terms, making it a binomial. A binomial consists of two terms separated by a plus or minus sign.

Add the polynomials:
(2x+5y) + (3x-2y)

• 3x + 5y

• 5x + 3y

• 5x + 7y

• 7xy + 1xy

Answer explanation

To add the polynomials (2x+5y) + (3x-2y), combine like terms: 2x + 3x = 5x, 5y - 2y = 3y. Therefore, the result is 5x + 3y.

(4x²+x) - (x²+2x)

• 3x² - x

• 4x² + 2x

• 3x² + 3x

• 3x² + 2x

Answer explanation

To simplify the expression, distribute the negative sign: 4x^2 + x - x^2 - 2x = 3x^2 - x. Therefore, the correct choice is 3x^2 - x.

Simplify the expression.
-3x²( 7x² - x + 4)

• -21x⁴ + 3x³ -12x²

• 7x² - x + 4 (-3x²)

• 21x⁴ + 3x³ + 12x²

• -12x² + 3x³ -21x⁴

Answer explanation

To simplify the expression, distribute -3x^2 to each term inside the parentheses. This results in -21x^4 + 3x^3 - 12x^2, which is the correct choice.

Multiply:
(4x+1)(5x−2)

• 20x² + 3x − 2

• 20x² − 11x + 5

• 20x² − 18x + 2

• 20x² − 3x − 2

Answer explanation

To multiply (4x+1)(5x−2), use the distributive property. Multiply each term in the first expression by each term in the second expression. Combine like terms to get 20x^2 - 3x - 2.

A rectangle has width (2x + 3) and length (2x - 4).  What is the perimeter of the rectangle?

• 4x - 12

• 4x - 1

• 8x - 2

• 4x² - 2x - 12

Answer explanation

To find the perimeter, add all sides: (2x + 3) + (2x + 3) + (2x - 4) + (2x - 4) = 8x - 2

Which of the following is a 5th degree trinomial with a leading coefficient of -2? 

• -2x⁵ + 3x - 1

• 5x^-2 +3x - 1

• -2x⁵ + 3x⁴ + 2x³ + x² - 10

• 2x + 5

Answer explanation

The correct choice is -2x^5 + 3x - 1 because it is a 5th degree trinomial with a leading coefficient of -2.