How to factor quadratic equations box method?

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Cooper Barker · Accepted Answer

For example: Factor       6          x      2        +    7    x    -    20  You have       a          x      2        +    b    x    +    c  Multiply ac  which, in this problem is             (      6      )              (      -      20      )        =    -    120  Find two numbers whose product is       a    c    =    -    120   and whose sum is       b    =    +    7  One number is positive and the other is negative because we want the product to be negative. The positive factor has a higher absolute value because we want the sum to be positive.We start the list:            (      -      1      )              (      120      )        the sum is not +7            (      -      2      )              (      60      )        the  sum is not +7            (      -      3      )              (      40      )        the sum is not +7            (      -      4      )              (      30      )        the sum is not +7            (      -      5      )              (      24      )        the sum is not +7            (      -      6      )              (      20      )       the sum is not +77 is not a factor            (      -      8      )              (      15      )       the sum is 7  Write       6          x      2        +    7    x    -    20    replacing       +    7    x   with       -    8    x    +    15    x        6          x      2        +    7    x    -    20    =    6          x      2        -    8    x    +    15    x    -    20   Now factor by grouping:            (      6              x        2            -      8      x      )        +          (      15      x      -      20      )        =    2    x          (      3      x      -      4      )        +    5          (      3      x      -      4      )        =          (      2      x      +      5      )              (      3      x      -      4      )      The &quot;factoring box&quot; is a technique for grouping factors.To use this box, you must first take out any factor that is common to all 3 terms. If we had started with       24          x      2        +    28    x    -    80   we would have to first factor out the 4 to get       4          (      6              x        2            +      7      x      -      20      )      Place the first and last terms in the main diagonal (upper left and lower right). Then, insert the two terms we discovered above, -8x and +15x, in the remaining two locations.             (                                    6                          x              2                                            +            15            x                                                -            8            x                                -            20                              )      Notice that each row has common factors and each column has common factors            (                                    6                          x              2                                            +            15            x                              )       has common factor 3xand             (                                    6                          x              2                                                            -            8            x                              )       has common factor 2xWe&#039;ll write those factors on a new first row and a new left column:            (                                              2            x                                +            5                                                3            x                                6                          x              2                                            +            15            x                                                -            4                                -            8            x                                -            20                              )      The factors are the top row and the left column:            (      2      x      +      5      )              (      3      x      -      4      )      Using a different boxIf we had put the -8x and 15x in the other 2 places.             (                                    6                          x              2                                            -            8            x                                                +            15            x                                -            20                              )                  (                                              3            x                                -            4                                                2            x                                6                          x              2                                            -            8            x                                                +            5                                +            15            x                                -            20                              )      The factors are             (      3      x      -      4      )              (      2      x      +      5      )

How to factor quadratic equations box method?

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