Dividing Polynomials by Binomials 2

Sometimes factoring polynomials is difficult or impossible.

Can these polynomials be divided by binomials?

can you factor x2 + 5x + 7?

(x + 3) (x + 2) + 1

NO!

Not factors!

So can you divide (x2 + 5x + 7) by (x+2)?

YES!....but it's ugly.

(x+3)(x+2) 1+ =(x + 2) (x + 2)

(x+3) + 1 (x + 2)

What if it is a really complicated polynomial that is really hard to simplify? Can it be divided?

YES!....but it's ugly

x3 + 3x2 + 3x + 1 (x+1)

x + 1 x3 + 3x2 + 3x + 1 x2

(x3 + x2)-

2x2 + 3x

+ 2x

(2x2 + 2x)-

x + 1

+ 1

(x + 1)-0

x2 + 5x + 7 (x + 2)

x2 + 5x + 7(x + 2)

4x3 - 1 + 8x 4 + 4x

4x + 4 4x3 + 0x2 + 8x - 1

6y3 - 4y2 - 9y - 3 2y2 - 3

a3 + 5a - 18 a -2

Assignment

exercise 8 1 - 4 and 8exercise 9 1- 8