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Factoring ax 2 + bx + c. Step 1: multiply the constant (c) term by the coefficient (a), of the leading term Constant is 6 Leading term is 6 Therefore.

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Presentation on theme: "Factoring ax 2 + bx + c. Step 1: multiply the constant (c) term by the coefficient (a), of the leading term Constant is 6 Leading term is 6 Therefore."— Presentation transcript:

1 Factoring ax 2 + bx + c

2 Step 1: multiply the constant (c) term by the coefficient (a), of the leading term Constant is 6 Leading term is 6 Therefore 6 * 6 is 36

3 Step 2: Rewrite the equation by replacing the constant with the number in step 1, and remove the leading coefficient. x x + 36

4 Step 3: Factor the new equation from step 2: x x +36 (x + 4)(x + 9)

5 Step 4: Divide each constant term in the factored form by the original coefficient of the leading term. Original coefficient of the leading term: 6

6 Then reduce the fractions:

7 Step 5: Now we use the “bottoms up” method- Move the denominator into the numerator to get:

8 Check it- use FOIL:

9 Remember you may check some equations using graphing calculator- type in the equation in y = and find where it crosses the x-axis. Not all equations cross the x-axis. This particular one crosses at x = -2/3 and x = -3/2. Look at these solutions and the end result of step 4, and then look at step 5. Factoring leads to solutions, the zeros, the roots.

10 Step 1: multiply the constant (c) term by the coefficient (a), of the leading term Constant is -3 Leading term is 10 Therefore -3 * 10 is -30

11 Step 2: Rewrite the equation by replacing the constant with the number in step 1, and remove the leading coefficient. x 2 - x - 30

12 SStep 3: Factor the new equation from step 2 : x 2 - x - 30 (x + 5)(x - 6)

13 Step 4: Divide each constant term in the factored form by the original coefficient of the leading term. Original coefficient of the leading term: 10 (x + 5)(x - 6) 10 10

14 Then reduce the fractions: (x + 1)(x - 3) 2 5

15 Step 5: Now we use the “bottoms up” method- Move the denominator into the numerator to get: (2x + 1)(5x – 3) (x + 1)(x - 3) 2 5

16 Check it- use FOIL: 10x 2 -6x + 5x – 3 10x 2 - x – 3 (2x + 1)(5x – 3)

17 6x 2 - 2x – 28 Step 1: multiply the constant (c) term by the coefficient (a), of the leading term Constant is -28 Leading term is 6 Therefore 6 * -28 is -168

18 Step 2: Rewrite the equation by replacing the constant with the number in step 1, and remove the leading coefficient. x 2 -2x -168

19 Step 3: Factor the new equation x 2 -2x -168 ( x -14 )(x +12 ) Factors of -168 Sum of factors -2, -84no -4, 42no -8, , 142 Switch -14, 12-2

20 Step 4: Divide each constant term in the factored form by the original coefficient of the leading term. Original coefficient of the leading term: 6 ( x -14 )(x +12 ) 6 6

21 Then reduce the fractions: ( x -7 )(x +2 ) 3 1 Step 5: Now we use the “bottoms up”

22 ( 3x -7 )(x +2 ) Check your answer with factoring (your choice). Conversation with a caution 6x 2 - 2x – 28 Purpose of factoring

23 Step 1: multiply (c) (a), Step 2: Rewrite the equation by replacing the constant with the number in step 1, and remove the leading coefficient. Step 3: Factor the new equation Step 4: Divide each constant term in the factored form by the original coefficient of the leading term and then reduce the fractions: Step 5: Now we use the “bottoms up”


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