Synthetic Division

​Synthetic Division

Synthetic Division is a shortcut for Long Division of Polynomials.

You get the same results either way, but Synthetic Division is faster and less confusing.

​In this lesson we are going to divide this polynomial by this binomial.

Multiple Choice

What are the coefficients we use?

• 5, 6, 28, 2

• 5, -6, -28, -2

• -5, 6, 28, 2

• -5, -6, -28, -2

Multiple Choice

What number do we put on the outside?

• -2

• 2

• -5

• 5

Multiple Choice

Is this the way to start?

• No, it should be a positive 2 on the outside.

• No, the coefficients are in the wrong order.

• yes

Multiple Choice

What is the first thing we do?

• Bring down the 5 below the line.

• Add all the coefficients

• Divide 5 by -2

• Multiply the 5 and 2

Multiple Choice

What goes next to the 5 below the line?

• 4

• -16

• 16

• -4

Multiple Choice

What goes under the -28?

• 32

• -32

• -20

• 20

Multiple Choice

What goes next to the 32?

• -4

• 4

• 8

• -8

Multiple Choice

What is the final answer?

• $$5x^{4\ }-16x^3+4x^2-10x$$

• $$5x^3-16x^2+4x-10$$

• $$5x^2-16x+4+\frac{10}{x+2}$$

• $$5x^2-16x+4-\frac{10}{x+2}$$