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Section 7.3 Products and Factors of Polynomials

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Factoring the Sum and Difference of Two Cubes

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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

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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

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

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

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

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

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Multiply the diagonals, add the columns. Add 15*3 = 45

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

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

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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.

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Divide a polynomial by a monomial.

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Divide the following numbers. Check

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Divide the following numbers (Long Division) Remainder

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

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

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

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

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

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Dividing a polynomial by a polynomial (Long Division)

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NOW YOU WRITE THIS ONE

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Dividing a polynomial by a polynomial (Long Division)

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Homework Problems 1. 2. 3. 4.

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