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Concept
(1)

Long division can be used to divide a polynomial by another polynomial, in this case a binomial of lower degree. When **dividing polynomials**, we set up the problem the same way as any long division problem, but are careful of terms with zero coefficients. For example, in the polynomial x^3 + 3x + 1, x^2 has a coefficient of zero and needs to be included as x^3+ 0x^2+3x+1in the division problem.

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Sample Problems
(11)

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Problem 1

How to factor trinomials when the leading coefficient has only one pair of factors.

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Problem 2

How to factor trinomials with the leading coefficient has more than one pair of factors.

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Problem 3

How to factor trinomials when the leading coefficient is negative.

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Problem 4

How to factor trinomials when a monomial can be factored out first.

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Problem 5

Factoring with an area, or rectangle method when "a" is not one

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Problem 6

A method for factoring trinomials that always works, even if "a" is not one: using a diamond, and then factoring by grouping

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Problem 7

Factoring trinomials where the "a" value is prime, using a guess and method

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Problem 8

Guess and check and FOIL method for factoring trinomials where the "a" value is not prime

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Problem 9

Factoring trinomials with a greatest common factor the results in "a" equaling one

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Problem 10

Factoring trinomials with GCF and "a" is not 1

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Problem 11

A geometric interpretation of factoring trinoimals that uses a length times width equals area rectangular model. A "diamond puzzle" is used to find the rectangle's sub-areas.