Vocab/Adding/Subtracting/Multiplying Polynomials

Polynomial Terminology

100

How many terms are in a monomial?

1

200

What is the constant term of 

4x-5+3x^2+77x^9

-5

300

Is this a polynomial? 

3x^2+4x^-1-6

No, because one of the terms has a negative exponent.

x^-1=1/x

which is division by a variable. A polynomial can have constants, variables and exponents,
but never division by a variable.

400

What is the leading term of the polynomial: 

5x^2+6x^9-5x

6x^9

because it is the term with the highest degree (biggest exponent on the variable). If you were going to write the polynomial in standard form, it would be written first. 

500

Write the following polynomial in standard form AND state the leading coefficient: 

9x-4+7x^3-2x^2

7x^3-2x^2+9x-4

The leading coefficient is 7 (the number in front of the variable with the largest power of x) 

Addition of Polynomials

100

(4x^2+2x) + (x^2+6x)

5x²+8x

200

(-3y^2+y) + (4y^2+6y)

y² +7y

300

(2a^2 - 7a + 10) + (a^2 + 4a + 7)

3a² -3a +17

400

(2r^2-5r+7)+(3r^3-6r)

3r^3 + 2r^2 -11r + 7

500

(5r^3-6r^2+3r) + (r^2-2r-3)

5r^3 - 5r^2 + r - 3

Subtraction of Polynomials

100

(y^2-10xy) - (2y^2+3xy)

-y^2-13xy

200

(2x^2 + 5x - 3) - (3x^3 + 2x - 5)

-3x³ + 2x² +3x + 2

300

(-3a^2-2a) - (4a^2-4)

-7a² - 2a + 4

400

(4x^3+5x+2) - (1+2x-3x^2)

4x³ + 3x² +3x + 1

500

(4-x-2x^2) - (-2+3x-x^3)

x³ - 2x² - 4x + 6

Multiply Monomials

100

(6x²)(5x)

30x³

200

(x²yz)(x²y⁴)

x⁴y⁵z

300

(3x²y)(5xyz)

15x³y²z

400

Simplify 2x(3xy) - 10x²y

-4x²y

500

(5x³y²)(x³y)(-2y)

-10x⁶y⁴

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

(x - 2)²

x² - 4x + 4 

500

(5b−6)(5b²+4b−2)

25b³ − 10b² − 34b + 12