Polynomials

Adding Polynomials

100

How many terms does this polynomial have? What is the formal name of it called? 3q+7+q

3 & Trinomial

200

Represent this polynomial using algebra tiles. 

(4 - 5p) - (-7p + 3)

2p + 1

300

Simplify this polynomial. (-3m²+4mn-n²) - (5m²+7mn+2n²)

-m²-3mn-3n²

400

Simplify this polynomial. -5s + st - 4s^2 - 12st + 10s - 2s^2

-6s^2 + 5s - 11st

500

Simplify (6a³+12a²-15a)-(4a²-12a+8)

6a³+8a²-3a-8

Identifying Polynomials

100

How many terms are there? 4x³-3x 

2

200

Name for 1 term (related to polynomials)

monomial

300

What dictates the end behavior of a polynomial?

ex: 4x²+10x-9

The leading term

400

Name 3 synonyms for x-intercepts

horizontal intercepts, roots, and zeroes

500

What is the leading term and the end behavior of 

-x²(-4x²-3x-11)(x-5)

-4x⁵  odd/negative

Multiplying Polynomials

100

Determine each product (2)(3x +4)

6x + 8x

200

Solve this polynomial (2r)(-6r)(18r²)

-216r⁴

300

Solve this polynomial (2x+3)(x+6)(x+5)

2x³+25x²+93x+90

400

Solve this mononmial (2xy)(2x^2 - 3xy + 7y^2)

4x^2 - 6xy + 14y^2

500

Solve this monomial (xy - x^2 + y^2)(-2)

2x^2 - 2xy - 2y^2

Dividing Polynomials

100

Solve this polynomial 8x+4/4

2x+1

200

Solve this polynomial   (n² + 5n − 50) ÷ (n − 5)

n + 10

300

Solve this polynomial -26c²+39c-13c/-13c

2c-3+1

400

(a³+ 13a²+39a−18) ÷ (a +6)

a²+7a−3

500

 (n²+ 10n + 18) ÷ (n + 5)

n + 5 − 7 /n + 5

Graphing Polynomials

100

What are the x-intercepts of the polynomial y=(x+3)(x+1)(x-5)?

x= -3, -1, 5

200

Name the y-intercept of the function x³+5x²−32x−7 and include what term is called that represents the y-intercept in standard form 

*bonus 100 points for another way to algebraically find the y-intercept 

-7 and the constant or the c term

*bonus substitute 0 for all x values and solve

300

Name each x-intercept and its multiplicity

y=(x-2)²(x+7)³

x=2 m=2, x=-7 m=3

400

What is the name of the term that determines how narrow or wide a quadratic will be? 

ex: y=1/2(x+2)(x+1)    y=2(x+2)(x+1)

the a value

500

We know that B(2)=0 and B(x)=3x²+15x-42. According to the remainder theorem, how can you prove this algebraically? and what will your answer tell you?

You can prove this algebraically by substituting 2 for each x and you will get 0. Because 0 is your answer  for y this proves that the factor x-2 is a factor of B(x)