Adding/Subtracting/Multiplying Polynomials

Addition of Polynomials

100

(4x² + 2x) + (x² + 6x)

5x² +8x

200

(-3y² + y) + (4y² + 6y)

y² +7y

300

(2a² - 7a + 10) + (a² + 4a + 7)

3a² -3a +17

400

(2r² - 5r + 7) + (3r³ - 6r)

3r³ + 2r² -11r + 7

500

(5r³ - 6r² +3r) + (r² -2r - 3)

5r³ - 5r² + r - 3

Subtraction of Polynomials

100

(y² - 10y) - (y² + 3)

-10y-3

200

(2x² + 5x - 3) - (3x³ + 2x - 5)

-3x³ + 2x² +3x + 2

300

(-3a² - 2a) - (4a² - 4)

-7a² - 2a + 4

400

(4x³ + 5x + 2) - (1 + 2x - 3x²)

4x³ + 3x² +3x + 1

500

(4 - x - 2x²) - (-2 + 3x - x³)

x³ - 2x² - 4x + 6

Classifying Polynomials

100

Rewrite in standard form. Classify each polynomial by degree and number of terms.

x²+5x⁴-1

5x⁴+x²-1

Quartic Trinomial 

200

Rewrite in standard form. Classify each polynomial by degree and number of terms.

x-2x²

-2x²+x

Quadratic Binomial

300

Rewrite in standard form. Classify each polynomial by degree and number of terms.

-3x+2x³+x²-1

2x³+x²-3x-1

Cubic Polynomial 

400

What is the leading coefficient and how many terms does this expression have?

4x²-3x+2-x⁴

The leading coeffiecent is -1 and it has 4 terms.

500

Is the following expression quadratic? Explain.

4x-4+x³

no the highest exponent is not 2. The expression is cubic.

Multiplying Polynomials

100

(x + 4)(x - 2)

x² + 2x - 8 

200

(a + 3)(a − 2)

a² + 1a − 6

300

(4m + 2)(4m + 5)

16m² + 28m + 10

400

(4x - 3)²

16x²-24x+9

500

(8n² + n − 4)(6n² − 6n − 4)

48n⁴ − 42n³ − 62n² + 20n + 16

Mixed Review

100

What is the the n^th coefficient?

3n²-6n+2

-6

200

What is the perimeter for a triangle whose side are:

2x+1

5x-4

x²+6

x²+7x+3

300

What is the area of a rectangle with a width of 2x - 1 and length of 3x+12

6x² + 21x - 12

400

Combine Like Terms:

(15x² + 6x - 3) – 2(10x² + 2x + 2)

-5x² + 2x - 7

500

Simplify:

(8x⁴ +11x³ - 6x + 5) + 2(-5x + 2x² + 10 - 6x⁴)

-4x⁴ + 11x³ + 4x² - 16x + 25