 # Section 7.3 Products and Factors of Polynomials.

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Section 7.3 Products and Factors of Polynomials

Factoring the Sum and Difference of Two Cubes

Factor Theorem (x-r) is a factor of the polynomial expression that defines the function P if and only if r is a solution of P(x) = 0, that is, if and only if P(r) = 0. In other words: – Set x-r = 0 – Solve for x. x = r – Plug this r in for every x in the original polynomial – Simplify – If you get 0 then (x – r) IS a factor of the polynomial

Let’s look at how to do this using the example: In order to use synthetic division these two things must happen: There must be a coefficient for every possible power of the variable. The divisor must have a leading coefficient of 1. #1#2

Step #1: Write the terms of the polynomial so the degrees are in descending order.

Step #2: Write the constant a of the divisor x- a to the left and write down the coefficients.

Step #3: Bring down the first coefficient, 5.

Step #5: After multiplying in the diagonals, add the column. Add the column

Step #7: Repeat the same procedure as step #6. Add Columns

The quotient is: Remember to place the remainder over the divisor.

Step #8: Write the quotient. The numbers along the bottom are coefficients of the power of x in descending order, starting with the power that is one less than that of the dividend.

Divide a polynomial by a monomial.

Divide the following numbers. Check

Divide the following numbers (Long Division) Remainder

Dividing a polynomial by a polynomial (Long Division) Check JUST WATCH THIS ONE!

Dividing a polynomial by a polynomial (Long Division) Check JUST WATCH THIS ONE!

Dividing a polynomial by a polynomial (Long Division) Check JUST WATCH THIS ONE!

Dividing a polynomial by a polynomial (Long Division) Check JUST WATCH THIS ONE!

Dividing a polynomial by a polynomial (Long Division) NOW YOU WRITE THIS ONE

Dividing a polynomial by a polynomial (Long Division)

NOW YOU WRITE THIS ONE

Dividing a polynomial by a polynomial (Long Division)

Homework Problems 1. 2. 3. 4.