BENNY MANDUJANO ALGEBRA 2 PROJECT - Polynomial Functions

Factoring Polynomials

100

Factor out completely.

x⁴+8x

x⁴+8x = x(x³+8)

          = x(x³+2³)

          = x(x+2)(x²-2x+4)

200

Factor out completely

49x⁴-9

49x⁴-9 = 7²x⁴-9

           = 7²x^2*2-9

           = 7²x^2*2-3²

               = 

300

Factor out completely

-3x³+12x²+15x

-3x³+12x²+15x

= -3x(x²-4x-5)

= -3x(x²-5x+x-5)

= -3x(x(x-5)+(x-5))

= -3x(x+1)(x-5)

400

Factor out completely

(3x²+2x)+(12x+8)

(3x²+2x)+(12x+8)

= x(3x+2)+4(3x+2)

= (x+4)(3x+2)

500

Factor out completely

3x²+6+2x+x³

3x²+6+2x+x³

= x³+3x²+2x+6

= x³+3x²+2x+6

= x²(x+3)+2(x+3)

= (x²+2)(x+3)

Dividing Polynomials

100

Find the quotient

(2x²+3x+1) / (x+2)

(2x²+3x+1) / (x+2)

=  2x-1 + (3/x+2)

             

200

Find the quotient

(4x³+5x²+5x+8) / (4x+1)

(4x³+5x²+5x+8) / (4x+1)

= x²+x+1+ (7/4x+1)

300

Find the quotient

(-5x⁵+0x⁴+0x³+0x²+0x-1) / (5x+5)

(-5x⁵+0x⁴+0x³+0x²+0x-1) / (5x+5)

= -x⁴+x³-x²+x-1+ (4/5x+5)

400

Find the quotient

(3x⁴+x³-17x²+19x-6) / (x²-2x+1)

(3x⁴+x³-17x²+19x-6) / (x²-2x+1)

= 3x²+7x-6

500

Find the quotient

(3x⁴+4x³-5x²+14x-17) / (x²+2x-2)

(3x⁴+4x³-5x²+14x-17) / (x²+2x-2)

= 3x²-2x+5- (7/x²+2x-2)

Adding Polynomials

100

Find the sum

(6x²+3x-4)+(x²-7)

(6x²+3x-4)+(x²-7)

= 7x²+3x-11

200

Find the sum

(3y²+5y-6)+(7y²-9)

(3y²+5y-6)+(7y²-9)

= 10y²+5y-15

300

Find the sum

(6a³+12a²-15a)+(4a²-12a+8)

(6a³+12a²-15a)+(4a²-12a+8)

= 6a³+16a²-27a+8

400

Find the sum

(-2x²-3x)+(2x+x²)

(-2x²-3x)+(2x+x²)

= -2x²+x²-3x+2x

= -x²-x

500

Find the sum

(2x²-3x+5)+(x²-3x+1)+(5x²-4x-8)

(2x²-3x+5)+(x²-3x+1)+(5x²-4x-8)

= 8x²-10x-2

Multiplying Polynomials

100

Find the product

-5x²(4x²+7x-3)

-5x²(4x²+7x-3)

= -20x⁴-35x³+15X²

200

Find the product

18x(22x²+8x-7)

18t(22t²+8t-7)

= 18t x 22t²+18t x 8t-18t x 7

= 396t³+18t x 8t-18t x 7

= 396t³+144t²-126t

300

Find the product

6x²y(5x+2)

6x²y(5x+2)

= 6x²y x 5x+6x²y x 2

= 30x³y+12x²y

400

Find the product

(25m+7)(3m²-3x+2)

(25m+7)(3m²-3x+2)

= 25m(3m²-3m+2)+7(3m²-3x+2)

= 75m³-75mx+50m+21m²-21x+14

500

Find the product

-2a⁴b³(6ab⁷+4ab-b²)

-2a⁴b³(6ab⁷+4ab-b²)

= 2a⁴b³ x 6ab⁷-2a⁴b³ x 4ab-2a⁴b³ x -b²

= -12a⁵b¹⁰-8a⁵b⁴+2a⁴b⁵

Subtracting Polynomials

100

Find the difference 

(5x-10)-(7x-9)

(5x-10)-(7x-9) = 5x-10-7x+9

                      = -2x-10+9

                      = -2x-1

200

Find the difference

(6-8x)-(2x²+4x+8)

(6-8x)-(2x²+4x+8) = 6-8x-2x²-4x-8

                             = -2x²-12x-2

300

Find the difference

(3m-3)-(8m+8)-(3m²+6m-7)

(3m-3)-(8m+8)-(3m²+6m-7) 

= 3m-3-8m-8-3m²-6m+7

= -11m-4-3m²

=-3m²-11m-4

400

Find the difference

(4x²-5xy-8y²)-(-7xy-6y²)-(2x²+3xy+7y²)

(4x²-5xy-8y²)-(-7xy-6y²)-(2x²+3xy+7y²)

= 4x²-5xy-8y²+7xy+6y²-2x²-3xy-7y²

= 2x²-xy-9y²

500

Find the difference 

(10x³+7x²-3x+2)-(x³-8x²-9x-12)

(10x³+7x²-3x+2)-(x³-8x²-9x-12)

= 9x³+7x²-3x+2+8x²+9x+12

= 9x³+15x²+6x+14