Geometry Support - Unit 1 Review

Classifying Polynomials

100

Identify: Is 5x a monomial, binomial, or trinomial?

5x is a monomial.

200

 Identify the degree and number of terms: 3x² + 7x

Quadratic Binomial

300

Identify: 4x³ − 2x + 1 — classify by number of terms and give degree.

Cubic Trinomial

400

True/False: x²y is a polynomial with one variable. Explain briefly.

False — x²y has two variables (x and y); it's a polynomial with two variables.

500

Identify: Name the polynomial type and degree for 

2x⁴ − 5x² + 3x − 7.

Quartic Polynomial

Adding Polynomials

100

Add: (2x + 3) + (x − 1)

(2x+3)+(x−1) = 3x + 2

200

Add: (4x² + x) + (3x² − 2x)

(4x²+x)+(3x²−2x) = 7x² − x

300

Add: (5xy + 2x) + (−2xy + 4x)

(5xy+2x)+(−2xy+4x) = 3xy + 6x

400

Add: (3x² − 2x + 5) + (−x² + 4x − 3)

(3x²−2x+5)+(−x²+4x−3) = 2x² + 2x + 2

500

Add: (2x³ + x² − x) + (−x³ + 3x − 4)

(2x³+x²−x)+(−x³+3x−4) = x³ + x² + 2x − 4

Subtracting Polynomials

100

 Subtract: (3x + 5) − (x + 2)

(3x+5) − (x+2) = 2x + 3

200

Subtract: (4x² + 2x) − (x² + x + 1)

(4x²+2x) − (x²+x+1) = 3x² + x − 1

300

Subtract: (5xy − 2x) − (3xy + x)

(5xy−2x) − (3xy+x) = 2xy − 3x

400

Subtract: (x³ + 4x² − x) − (2x³ − x² + 3x)

(x³+4x²−x) − (2x³−x²+3x) = −x³ + 5x² − 4x

500

Subtract: (3x² − 5x + 2) − (−x² + 4x − 1)

(3x²−5x+2) − (−x²+4x−1) = 4x² − 9x + 3

Multiplying Polynomials

100

Multiply: x(3x + 2)

 x(3x+2) = 3x² + 2x

200

Multiply: 2x( x² + 3 )

2x(x²+3) = 2x³ + 6x

300

Multiply (FOIL): (x + 2)(x + 3)

 (x+2)(x+3) = x² + 5x + 6

400

Multiply: (x − 4)(x + 5)

(x−4)(x+5) = x² + x − 20

500

Multiply (with two variables): (2x − y)(x + 3y)

(2x−y)(x+3y) = 2x² + 5xy − 3y²

Mixed Review

100

Classify: How many terms and what degree is 6x?

Linear Monomial

200

Add then Classify: Add (x + 2) + (2x − 5). Then say whether the result is a monomial, binomial, or trinomial.

(x+2)+(2x−5) = 3x − 3 = Binomial

300

Multiply then Simplify: x(2x + 3) + (x + 1). First multiply, then add like terms.

 x(2x+3) + (x+1) = 2x² + 3x + x + 1 = 2x² + 4x + 1

400

Subtract then Classify: (4x² + x − 3) − (x² + 2x + 1). State the degree of the result.

  (4x² + x − 3) − (x² + 2x + 1) = 3x² − x − 4 = degree 2 (Quadratic)

500

Mixed multi-step: (1) Multiply (x + 2)(x − 3). (2) Add 4x to your result. (3) Classify the final polynomial (number of terms and degree).

(x+2)(x−3) = x² − 3x + 2. Add 4x: x² + x + 2. Final: Quadratic Trinomial