Factoring ax2 + bx + c.ppt - Elkatanani by huanghengdong

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									         Five Minute Focus

1. Factor x2 – 4

2. Factor x2 + 8x + 16

3. Multiply (x + 3)(x + 5)

4. Multiply (x – 2)(x – 7)
      6.4 Factoring x2 + bx + c
CA Standard 11.0 Apply basic factoring techniques to second degree
polynomials.


What You Will Learn
-    To factor trinomials of the
    type x2 + bx + c where c > 0
-    To factor trinomials of the
    type x2 + bx + c where c < 0
                                         … and Why??
                                         - To factor more
                                         trinomials
Factoring: ax2 + bx + c
To determine the factors of this
problem, we’ll make a diamond      Ex.
problem. Multiply a & c and
put into the top part of the       Factor. 1x2 + 8x + 15
diamond, then take the “b”
coefficient and put it in the
                                    (x+ 3 )(x+ 5 )
bottom part of the diamond.
You will need to find factors so
that when multiplied together                15
you get ac and when added                3         5
together you get b.
                                             8
              ac


               b
Factoring: ax2 + bx + c                         ac

Remember it’s the product of a&c,
but the sum of b to find the factors.           b


 Factor.   1m2 + 7m + 12         Factor.    1x2 + 9x + 8


   (x+ 3 )(x+ 4 )                 (x+ 1 )(x+ 8 )

            12                              8
       3            4                   1            8

             7                              9
Factoring: ax2 + bx + c                            ac

Remember it’s the product of a&c,
but the sum of b to find the factors.              b


 Factor.    b2 - 6b + 9          Factor.     a2 - 14a + 48


   ( x - 3 ) ( x - 3)             ( x - 6) ( x - 8 )

              9                              48
       -3          -3                   -6              -8

                                             -14
              -6
Factoring: ax2 + bx + c                            ac

Remember it’s the product of a&c,
but the sum of b to find the factors.              b


 Factor.    x2 - 6x - 16         Factor.     a2 - 14a + 45


   ( x + 2) ( x - 8)              ( x - 5) ( x - 9 )

            -16                              45
        2          -8                   -5              -9

             -6                              -14
Factoring: ax2 + bx + c                             ac

Remember it’s the product of a&c,
but the sum of b to find the factors.               b


 Factor.    y2 - xy - 2x2        Factor.       b2 - 5bc - 24c2


   ( y + x) ( y - 2x )            ( x - 3c) ( x + 8c)

                                              -24c2
            -2x2
        x          -2x                  -3c              8c

              x                                5c
         6.4 Factoring x2 + bx + c
               pg. 276-277

1. x2 + 8x + 15       3. x2 + 7x + 12         5. x2 – 6x + 9

7. x2 + 9x + 14       9. b2 + 5b + 4          11. a2 – 14a + 48

13. m2 + 10m + 21     15. z2 – 10z + 24

17. a2 – 9ab + 20b2     19. c2 – 7cd + 10d2

21. y2 – 11yz + 10z2 23. x2 + x – 42          25. x2 – 7x – 18

								
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