MAT121 - Polynomials & Factoring (Ch. 5 & 6)

Adding & Subtracting

100

(5y^2+12y+4)+(6y^2-8y+7)

11y^2+4y+11

200

(7x^2-2xy+6y^2)+(3x^2-5xy)

10x^2-7xy+6y^2

300

(a^2-b^2)-(a^2+3ab-4b^2)

-3ab+3b^2

400

Subtract

(5x^2-x+12)

 from  

(9x^2-6x-20)

4x^2-5x-32

500

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

x^3+y^3+2x^2y-5xy^2

Multiplying & Dividing

100

(3r-8)(11r+1)

33r^2-85r-8

200

(y+8)(4y^2+y-7)

4y^3+33y^2+y-56

300

(48y^4-24y^3) div (-8y^2)

-6y^2+3y

400

(2x^3+6x^2-15x+21) \div (x+5)

2x^2-4x+5+(-4)/(x+5)

500

(2n^3-10n+28) div (2n+4)

n^2-2n-1+32/(2n+4)

Exponent Properties

100

p^21/p^7

p^14

200

2/c^-5

2c^5

300

(5/8 x^3y)(24x^5y)

15x^8y^2

400

(-5m^4n^6)(8m^-5n^-3)

-(40n^3)/m

500

((2ab^2)/c)^-3

c^3/(8a^3b^6)

Factoring

100

-18xy^2-27x^2y

-9xy(3x+2y)

200

p^2+11p+30

(p+5)(p+6)

300

5x^2-17x+6

(5x-2)(x-3)

400

5x^3-3x^2+5x-3

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

500

250r^3+54

2(5r+3)(25r^2-15r+9)

Random

100

Classify by degree and number of terms:

y^2+6y^3+9y^4

4th degree trinomial

200

Write the formula for factoring a difference of cubes.

a^3-b^3

Remember "Same, Opposite, Always Positive" (S.O.A.P.) for the signs.

(a-b)(a^2+ab+b^2)

300

A painter drops a brush from a platform 75 feet high. The function 

h(t)=-16t^2+75

gives the height of the brush t seconds after it was dropped. Find the height after 2 seconds.

After 2 seconds, the height of the brush is 11 feet.

400

Solve:

5a^2-26a=24

a=-4/5 or 6

500

Find the x- and y-intercepts of the function:

f(x)=6x^2-7x-5

x-int: 

(5/3,0), (-1/2,0)

y-int: (0, -5)