Polynomials Test Review

Notes

100

You ADD the exponents when variables are ________.

Multiplied

200

When dividing variables, what do you do with the exponents?

Subtract

300

When exponents are stacked, for example:  (x²)⁴ , you ________ the exponents.

Multiply

400

When factoring a perfect square trinomial, ex: x²+10x+25 , what should be the first thing you do to start factoring?

Take the square root of the last number 

500

In the FOIL method, what does "O" stand for? For the following expression, which two terms would you multiply for "O"?  (x-3)(2x+5)

Outer/Outside, -3 and 5

Adding/Subtracting

100

(x³-5x+1) + (2x³+2x+4) =

3x³-3x+5

200

(b²+4b+7)+(b²-b+2) =

2b²+3b+9

300

(x²-2x+6)-(x²+2x-2) =

-4x+8

400

(3x⁵-2x³+5x-2)+(3x⁵+8x³+2x²-2x-5) =

6x⁵+6x³+2x²+3x-7

500

(5r⁴+4r²-2r+9)-(2r⁴-2r²+4) =

3r⁴+6r²-2r+5

Exponent Rules

100

(x³)(x⁴) =

x⁷

200

(y⁹)/(y³) =

y⁶

300

(3x⁵)² =

9x¹⁰

400

(5x³-10x²+25x) / (5x) =

x²-2x+5

500

(15x⁴y²z)(3x²yz⁴) =

45x⁶y³z⁵

Factoring

100

Find the GCF for (2x⁴-4x)

GCF = 2x

200

Find the GCF for (27x²y+6x²y²)

GCF = 3x²y

300

Factor: (x²-6x+9)

(x-3)(x-3)  OR  (x-3)²

400

Factor: (y²-81)

(y+9)(y-9)

500

Factor: (12x⁵y³z²-36x⁴y²z+28x³y²z)

4x³y²z(3x²yz-9x+7)

Distribute/FOIL

100

6x(2x-3) =

12x²-18x

200

3xy(2x+5y) = 

6x²y+15xy²

300

(x-2)(x+4) = 

x²+2x-8

400

(2y-3)(4+y)

2y²+5y-12

500

(3xz-5y)(2xy+z)

6x²yz+3xz²-10xy²-5yz