Quotient of a Polynomial - Synthetic Division

Quotient of a Polynomial

Dividing polynomial expressions with synthetic division.

It starts...

Let's see if you remember difference of squares....

Multiple Choice

x² + 81

• Unfactorable

• ( x - 9 ) ( x + 9 )

• ( x + 9 ) ( x + 9 )

• ( x - 9 ) ( x - 9 )

Multiple Choice

4x² - 64y²

• Unfactorable

• ( 2x - 32y) (2 x + 32y)

• ( 2x - 8y) (2 x - 8y)

• ( 2x - 8y) (2 x + 8y)

Multiple Choice

x² - 225

• ( x + 15) ( x + 15)

• Unfactorable

• ( x - 15) ( x + 15)

• ( x - 15) ( x - 15)

Synthetic Division

 $\frac{2x^2+7x+9}{x+2}$  

Step 1:  Write the coefficients of the dividend 2, 7, 9.  In the top left corner write the value for the divisor (x - a), so a = -2.  Copy the coefficient in the dividend below the horizontal bar.

Synthetic Division (Cont)

 $\frac{2x^2+7x+9}{x+2}$  

Step 2:  Multiply the first coefficient by the divisor (2 (-2) =-4).  Write the product under the next coefficient.  (-4 goes under 7)

Repeat step 2 until all additions have been completed in all columns.

Synthetic Division (Cont)

 $\frac{2x^2+7x+9}{x+2}$  

Step 3: The quotient is represents by the numbers below the horizontal bar.  (2, 3 and 3).  The boxed number is the remainder, the others are the coefficients of the polynomial quotient in decresing degrees.

Another Example:

Multiple Choice

What should be the order of the polynomial ?  

(Remember the polynomial must be in order by highest degeree)

 $\frac{3x-4x^3+6x^4+1}{x+3}$  

• 3  0  -4  6  1

• 6  -4  3  1  0

• 6  -4  0  3  1

• -6  4  0  -3  -1

Multiple Choice

For synthetic division, what would be the number in the left hand box?

• 0

• 1

• 2

• 3

Multiple Choice

For synthetic division, what would be the terms on the right hand side?

• 0 12 20 96

• 1 12 20 -96

• 3 2 1 0

Multiple Choice

For synthetic division, what would be the number in the left hand box?

 $\frac{x^2-6x+8}{x-2}$  

• 2

• -6

• 8

• -2

Multiple Choice

For synthetic division, what would be the terms on the right hand side?

 $\frac{x^2-6x+8}{x-2}$  

• 0  -6  8

• 2  -6  8  -2

• 1  -6  8

• 2  1  0

Multiple Choice

 $\frac{x^2-6x+8}{x-2}$  

• x-6

• x-9 R=2

• x-4

• x-8 R=3

Multiple Choice

• x - 7
• x² - 7
• x + 7
• x² + 3x - 54

You got this!

Try a few of these on your own.

Multiple Choice

-2x²+4x+48 ÷ x+4

• -2x+12
• 2x+12
• -4x+9
• 4x+9

Multiple Choice

When can we use Synthetic Division to divide polynomials?

• Any time we need to divide.

• When dividing by a binomial

• When dividing by any polynomial.

• Only when dividing by a linear factor with a leading coefficient of 1

Multiple Choice

The answer to a division problem is known as the...?

• product
• sum
• difference
• quotient

Multiple Choice

If 𝒙²+𝟑𝒙+𝟕 is divided by  𝒙+𝟐, then what is the remainder?

• 0
• -3
• 9
• 5

Poll

Just Breath....Everything will be ok. How are you feeling?

• Im doing ok

• I need a little more time