By Gurshan Saran. FACTORING Now check, how many terms? Afterward, ask yourself, Is there a GCF? The first thing you should always do if it has not been.

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Presentation transcript:

By Gurshan Saran

FACTORING Now check, how many terms? Afterward, ask yourself, Is there a GCF? The first thing you should always do if it has not been done is: Put it in proper order ( 3x 2 + 9x + 12) Yes? How to Factor Out an GCF 1.Find a greatest common factor for all of the terms 2. Prime Factor and take all of the common bases with the lowest exponent **Also note that if the 1 st term is negative, we should factor out a negative with the GCF 3. Divide each term by the GCF and put it inside the brackets. Write the GCF outside of the brackets set Example -3x xy Common base = -3, Lowest exponent = x -3x ( -3x x 15xy ) x = -3x (x 2 +3y) NO?

2 TERMS ? Difference of Squares TERMS ?4 TERMS ? Easy Quadratic? 1x 2 + 4x + 8 Hard Quadratic? (3x x + 21) Decomposition Factoring By Grouping 4x 2 + 4x + 8x + 2

Difference of Squares Factoring They have 2 terms that are perfect squares and are subtracted! 1.Draw 2 sets of brackets 2. Take the square root of both terms and put in both brackets 3. Separate with a + in one and a – in the other Example: Factor: 9x 2 – 16y 2 ( ) (3x 4y) (3x+4y) (3x-4y)

Factoring Easy Quadratics (a=1) 1.Now, look at the last term and the middle term and think what 2 numbers multiply to get the last term and add to get the middle term 2.Now, draw a set of brackets 3. Put an x in each bracket and then just simply put those values that you found Example: Factor x x + 16 Lets try 8 & 2. 8 x 2 = 16 (our last term) and = 10 (our middle term) It works! ( ) (x+2) (x+8)

Factoring Hard Quadratics (a 1) In this example, I am using the decomposition method 1.Multiply the 1 st term and the last term and get a product 2.Find 2 numbers that multiply to this product and add to the middle term 3.Replace the middle term with those 2 terms 4. Now we can easily factor this by grouping Example: Factor 6x x + 4 Product = 24 Two numbers that multiply to 24 and add to 11 are 8 & 3 = 6x 2 + 3x + 8x + 4 2(3x+4) +1(3x+4) =(2x+1)(3x+4)

Factoring By Grouping (4 term expressions) 1.Here we have 4 terms. First factor the first 2 terms and the last 2 terms. 2.Now you can check if you did this right because both brackets should be the same. 3.Now you can group together the terms outside the brackets and then all you are left with is the common factor that’s in the brackets. Now this becomes a FOIL type question and it is done Example: Factor 2x 2 + 4x + 6x x(x+2) +6(x+2) (2x+6) (x+2) Once you are finished ANY factoring problem, you can check it by using FOIL and multiplying out the brackets. Thanks for watching!