Review of Polynomials

Classifying Polynomials

100

Is the following a polynomial function?

-2x³+5x+7

Yes

200

Is the following a polynomial?
-x²+7x^-1+x

No

300

Write the following in standard form AND determine its degree and leading coefficient.

x³-6x-5x⁴

-5x⁴+x³-6x

D:4

LC: -5

400

Write the following in standard form AND determine its degree and leading coefficient.
-1-0.5x²+3x+11x⁴+x⁵

x⁵+11x⁴-0.5x²+3x-1

D: 5
LC: 1

500

What type of polynomial is this?

-1-0.5x²+3x+11x⁴+x⁵

Quartic

Adding/Subtracting Polynomials

100

(3x³+2x²-x-7)+(x³-10x²+8)

4x³-8x²-x+1

200

(9y³+3y²-2y+1)+(-5y²+y-4)

9y³-2y²-y-3

300

(2x³+6x²-x+1)-(8x³-3x²-2x+9)

-6x³+9x²+x-7

400

(3z²+z-4)-(2z²+3z)

z²-2z-4

500

-1-(5t³-t²+17)

-5t³+t²-18

Multiplying Polynomials

100

(4n+5)(4n-5)

16n²-25

200

(5a+2)²

25a²+20a+4

300

(4x²+x-5)(2x+1)

4x³+6x²-9x-5

400

(m-2)(m-1)(m+3)

m³-7m+6

500

(xy-3)³

(xy)³-9(xy)²+27xy-27

Dividing Polynomials

100

x³-6x²+7x+6

x²-3x-2

200

(x⁴+x³-11x²-5x+30) / (x-2)

x³+3x²-5x-15

300

(x²+8x+1) / (x-4)

x+12+49/(x-4)

400

(4x²-13x-5) / (x+2)

4x-21+37/(x+2)

500

(x⁴+4x³+16x-35) / (x+5)

x³-x²+5x-9+10/(x+5)

Factoring Polynomials

100

x³-4x²-5x

x(x-5)(x+1)

200

3y⁵-48y³

3y²(y-4)(y+4)

300

z³+5z²-4z-20

(z-2)(z+2)(z+5)

400

a³+27

(a+3)(a²-3a+9)

500

3r⁶-11r⁵-20r⁴

r⁴(r-5)(3r+4)