Question

You have learned how to divide polynomials in three different ways: by factoring, by long division, and by synthetic division. Explain in words and with mathematical representations how you would divide this polynomial in each of the three ways:
a) Factoring:
b) Long division:
c) Synthetic division:
d) Now, explain a connection you can see for each pair of methods. How does factoring relate to long division? How does long division relate to synthetic division? How does synthetic division relate to factoring?

Answer 1

The way to solve the polynomial using the methods is given below.

How to explain the polynomial?

Polynomial by factoring:

An example is (t² + 5t + 4) / +t + 4)

= (t + 1)(t + 4)/(t + 4)

= t + 1.

Dividing polynomial by long division:

Divide the first term of the dividend by the first term of the divisor.

Put this as the first term in the quotient.

Subtract to create a new polynomial.

Continue until you can't divide anymore.

Dividing polynomial by synthesic division:

Step 1: Set up the synthetic division.

Step 2: Bring down the leading coefficient to the bottom row.

Step 3: Multiply c by the value just written on the bottom row.

Step 4: Add the column created in step 3.

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