Factoring

Factoring- the resolution of an entity into factors such that when multiplied together they give the original entity

Factor- One of two or more quantities that divides a given quantity without a remainder. (2 and 3 are factors of 6)

GCF= Greatest common factor.


 * Basic Factoring**

4abz + 2ab Factor out the GCF. 4abz + 2ab = (2ab)(2z +1)

21abxz + 7ayz = (7az)(3bx + y)


 * Factoring Trinomials**

When we factor quadratics, the standard form is a x2 + bx + c.

x2 + 5x + 6 To factor a basic quadratic like this one, you need to find factors of 6 that add up to 5. Since 6 can be written as the product of 2 and 3, and since 2 + 3 = 5, the only way to factor this is to use 2 and 3. x2 + 5x + 6 = (x + 2)(x + 3)

An example using negatives: x2 – 5x – 6 = (x – 6)(x + 1)

Sometimes, a quadratic will not be able to factor. x2 + 7x – 6 There is no pair of factors of –6 that will add to +7. This means the quadratic is “prime”.

When the coefficient of x2 is not 1, the same rules apply. Find factors of the product of “a” and “c”. 2 x2 + x – 6 = (2x – 3)(x + 2)

Watch out for your signs when a problem has negatives in them.

*You can always check your work by multiplying your answer back out and finding the original problem. ­ Answer: (x + 2)(x + 3) Check by FOIL. x2 + 5x + 6


 * Links**

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