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Factoring ax 2 + bx + c. “Bottoms Up”. 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. 6 x 2 + 13x + 6. - PowerPoint PPT Presentation
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“BOTTOMS UP”
Factoringax2 + bx + c
6X2 + 13X + 6Step 1: multiply the constant (c) term by
the coefficient (a), of the leading term Constant is 6 Leading term is 6Therefore 6 * 6 is 36
6X2 + 13X + 6 Step 2: Rewrite the equation by replacing
the constant with the number in step 1, and remove the leading coefficient.
x2 + 13x + 36
Step 3: Factor the new equation from
step 2: x2 + 13x +36
(x + 4)(x + 9)
(X + 4)(X + 9)
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
Then reduce the fractions:
Step 5: Now we use the “bottoms up”
method- Move the denominator into the numerator to get:
Check it- use FOIL:
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.
10X2 - X - 3Step 1: multiply the constant (c) term by
the coefficient (a), of the leading term Constant is -3Leading term is 10Therefore -3 * 10 is -30
10X2 - X - 3 Step 2: Rewrite the equation by replacing
the constant with the number in step 1, and remove the leading coefficient.
x2 - x - 30
X2 - X - 30
Step 3: Factor the new equation from step 2: x2 - x - 30
(x + 5)(x - 6)
(X + 5)(X - 6)
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
Then reduce the fractions:
(x + 1)(x - 3) 2 5
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
Check it- use FOIL:
10x2 -6x + 5x – 3
10x2 - x – 3
(2x + 1)(5x – 3)
YOU TRY!6x2 - 2x – 28
Step 1: multiply the constant (c) term by the coefficient (a), of the leading term
Constant is -28Leading term is 6Therefore 6 * -28 is -168
6X2 - 2X – 28
Step 2: Rewrite the equation by replacing the constant with the number in step 1, and remove the leading coefficient.
x2 -2x -168
Step 3: Factor the new equation
x2 -2x -168
( x -14 )(x +12 )
Factors of -168
Sum of factors
-2, -84 no-4, 42 no-8, 21 13-12, 14 2Switch-14, 12 -2
( X -14 )(X +12 )
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
( X -14 )(X +12 ) 6 6
Then reduce the fractions:
( x -7 )(x +2 ) 3 1
Step 5: Now we use the “bottoms up”
( 3x -7 )(x +2 )Check your answer with factoring (your choice).
Conversation with a caution6x2 - 2x – 28
Purpose of factoring
QUICK STEPS!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 equationStep 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”