Polynomials

Synthetic Division.

100

( 6x+ 5) ÷ ( x + 1) 

 6 - 1/x+ 1

200

(x² +6x +5)  ÷ ( x +5)

x +1 

300

(x² - 3x - 4)  ÷ ( x - 2)

x -1 - 6/ x -2

400

(x³ + 3x² +5x+2) ÷ (x + 2)

x² + x+ 3 - 4/ x+ 2

500

(-x³ - 4x² - 5) ÷ (x + 3)

-x² -x + 3 - 14/x+3

Finding Remainder.

100

Find the remainder when

 (2x + 4)  ÷ (x + 2)

R = 0 

200

Find the remainder when

 (x²+ 8x + 1)  ÷ (x - 4)

R = 49

300

Find the remainder when

 (2x³ - 5x²-8x + 15)  ÷ (x - 3)

R = 0

400

Find the remainder when

 (x⁴ + 4x³ +16x -35)  ÷ (x + 5)

R =10

500

Find the remainder when

 (-x⁴ - 3x³ - x² - 2x - 5)  ÷ (x + 5)

R = -270 

Finding K

100

Find K when  (4x + k) ÷          ( x - 1) has a remainder of 6.

 K = 2 

200

Find K when (- 5x + k)    ÷     ( x + 2) has a remainder of 4.

K = -6 

300

Find K when (x² - 5x + k)      ÷       ( x + 3) has a remainder of 0.

K = -24

400

Find K when (x³ - x² -3x + k) ÷   ( x + 5) has a remainder of 52.

K=187

500

Find K when (x⁴ - 5x³ - kx -3) ÷   ( x - 2) has a remainder of 3.

k = -15

Factorization special Product Patterns.

100

Factorize x² - 9 

( x + 3) (x - 3) 

200

Factorize x² + 36 

(x - 6i) (x + 6i)

300

Fcatorize 4x² - 81

( 2x - 9) ( 2x + 9)

400

Factorize 16x² + 49

( 4x + 7i) (4x -7i) 

500

Factorize x³- 8

(x - 2) ( x² + 2x + 4)

Factorization completely or grouping

100

Factorize  4x -20 

4 (x -5)

200

Factorize completely  x³ + 2x² + x

x(x +1 ) (x + 1) 

300

Factorize by grouping 

x^{3 -} 8x² - 4x +  32

(x - 2) (x + 2) ( x - 8)

400

Factorize completely 

2x³ - 4x² -30x

x ( x -5)(x+ 3)

500

Factorize by grouping 

x³ + 2x² - 36x - 72

(x + 2) (x + 6) ( x - 6)