Polynomials

Identifying Polynomials

100

What is the degree of this polynomial?

5x² + 4x + 1

2

200

What is the constant of this polynomial?

4p⁵ - 9p⁴ + p³ + 4

4

300

Is this expression a polynomial?

g² + 3g^-1 + 5

No

400

What is the leading coefficient of this polynomial?

12x⁵ + 4x³ - 5

12

500

Classify this polynomial by its number of terms. 

(monomial, binomial, trinomial)

4u² - 3u² + 34u

binomial

Adding and Subtracting

100

Simplify the expression.

(x + 2) + (4x + 5)

5x + 7

200

Simplify the expression.

(4x + 12) - (3x + 5)

x + 7

300

Simplify the expression.

(3m² - 12m + 5) + (2m² + 3m - 6)

5m² - 9m - 1

400

Simplify the expression.

(15t - 4t² + 2) - (3 + 4t² + 6t)

-8t² + 9t - 1

500

Simplify the expression.

(-2y + 3y³ + 5) - (2 + 3y + 5y²)

3y³ - 5y² - 5y + 3 

Multiplying by Monomials

100

Simplify the expression.

3(x + 5)

3x + 15

200

Simplify the expression.

4v(v + 9)

4v² + 36v

300

Simplify the expression.

-4x²(5x² + 6x + 2)

-20x⁴ - 24x³ - 8x²

400

Simplify the expression.

4r(5r - 3) + r(r + 3)

21r² - 9r

500

Simplify the expression.

3p²(4p + 9 + 5p²) - 6p(5 + 3p² - 10)

15p⁴ - 6p³ + 27p² + 30p

Multiplying by Polynomials

100

Simplify the expression.

(x + 2)(x + 5)

x² + 7x + 10

200

Simplify the expression.

(3x - 7)(8x + 12)

24x² - 6x -84

300

Simplify the expression.

(9y² + 15)(6y - 10)

54y³ - 90y² + 90y - 150

400

Simplify the expression.

(3x + 2)(x² + 15x + 2)

3x³ + 47x² + 36x + 4

500

Simplify the expression.

(9x + 3 + x²)(10 - 4x² + 31x)

-4x⁴ - 5x³ + 277x² + 183x + 30

Special Cases

100

Simplify the expression.

(x + 3)²

x² + 6x + 9

200

Simplify the expression.

(4t + 2)²

16t² + 16t + 4

300

Simplify the expression.

(4r - 5)²

16r² - 40r + 25

400

Simplify the expression.

(2y + 6)(2y - 6)

4y² - 36

500

Simplify the expression.

(3f + 9)(3f - 9) + (f + 3)²

10f² + 6f - 72