polynomials

polynomials

100

decide whether the function is a polynomial function. if so, write it in the standard form and state its degree, type, leading coefficient 

f(x)= -3x+5x³-6x²+2

f(x)=5x³-6x²-3x+2

degree:3

type:cubic

leading coefficient: 5

200

decide whether the function is a polynomial function. if so, write it in the standard form and state its degree, type, leading coefficient 

f(x)= 9x⁴+8x³-6x²+2x

not a polynomial 

300

evaluate the function for the given value of x

h(x)= -3x⁴+2x³-12x-6;x=-2

h(x)=-46

400

describe end behavior

h(x)= -5x⁴+7x³-6x²+9x+2

the function has an even degree and a negative leading coefficient 

f(x)=-∞ as x -∞

f(x)=-∞ as x ∞

500

describe the end behavior 

g(x)= 7x⁷+12x⁸-6x³-2x-18

the degree is odd and the leading coefficient is positive 

g(x)= -∞ as x -∞

g(x)= ∞ as x ∞ 

subtracting

100

(2x³+6x²−x+ 1)-(8x³− 3x²− 2x+ 9)

6x³− 9x²−x + 8

200

(3z²+z− 4)-(2z²+ 3z)

−z²+ 2z+ 4

300

(3x³-2x²+4x-8)-(5x³+12x²-3x-4)

-2x³-14x²+7x-4

400

(7x⁴-9x³-4x²+5x+6)-(2x⁴+3x³-x²+x-4)

5x⁴-12x³-3x²+4x+10

500

(5x⁶-2x⁴+9x³+2x-4)-(7x⁵-8x⁴+2x-11)

5x⁶-7x⁵+6x⁴+9x³+7

adding

100

(x³ - 7x² + 6x⁴)+(-6x⁴ + x³ + 3x²)

2x²-4x²

200

(n⁵-6-7n⁴)+(8n⁵-n⁴-6n³)

9n⁵-8n⁴-6n³-6

300

(4a⁴-2a³+7a²)+(-6a²-2a³+5a⁴)

9a⁴+a²

400

(-8k+3k³-k⁴)+(-8k³+8k²-4k)

10m⁵-3m³-15

500

(3x³+ 2x²−x− 7)+(x³− 10x²+ 8 )

4x³−  8x²−x + 1

multiplying

100

 (y+ 5) (3y²− 2y+ 2)

3y³+ 13y²− 8y+ 10

200

(−x²+ 2x+ 4) (x− 3)

3x²− 6x − 12

300

(x− 1) (x+ 4) (x+ 5) 

x³+ 8x²+ 11x − 20

400

(2x+4)(2x²-8x+3)

4x³-8x²-26x+12

500

(3x+4)(7x²+2x-9)

21x³+34x²-19x-36

vocabulary

100

what is a polynomial 

is a monomial or a sum of monomials 

200

end behavior 

 a function’s graph is the behavior of the graph as x approaches positive infinity (+∞) or negative infinity (−∞).

300

pascals triangle 

When you arrange the coefficients of the variables in the expansion of (a+b)ⁿ, you will see a special pattern

400

polynomial function 

is a function of the form f(x)=aⁿ xⁿ+a_n−1x^n-1+⋅⋅⋅ +a₁x+a₀ 

500

quadratic function 

is a polynomial function with one or more variables in which the highest-degree term is of the second degree