Factor completely: " inputq = "x2" if B > 0: if B != 1: inputq += " + %dx" % B else: inputq += " + x" else: if B != -1: inputq += " - %dx" % (B*-1) else: inputq += " - x" if C > 0: inputq += " + %d" % C else: inputq += " - %d" % (C*-1) string += inputq +"
" string += "First, determine all integer pairs whose product is %d and then compute each sum.
" % C string += "Integer pairs whose product is %d | " % C for i in range(length): if sl[i] != B: string += "%d,%d | " % (pwholist[i][0],pwholist[i][1]) else: string += "%d,%d | " % (pwholist[i][0],pwholist[i][1]) a = pwholist[i][0] b = pwholist[i][1] string += "
Sum | " for i in range(length): if sl[i] != B: string += "%d | " % sl[i] else: string += "%d | " % sl[i] string += "
Since %d is the coefficient of the middle term, " % B string += inputq + " = " if a > 0: p1 = "(x + %d)" % a else: p1 = "(x - %d)" % (a*-1) if b > 0: p2 = "(x + %d)" % b else: p2 = "(x - %d)" % (b*-1) if p1 != p2: string += p1 + p2 + "
" else: string += p1 + "2" string += "" print string return /// CPU time: 0.00 s, Wall time: 0.00 s }}} {{{ visual_factor_BCform(-7,12) ///Factor completely: x2 - 7x + 12
First, determine all integer pairs whose product is 12 and then compute each sum.
Integer pairs whose product is 12 | 1,12 | -1,-12 | 2,6 | -2,-6 | 3,4 | -3,-4 |
Sum | 13 | -13 | 8 | -8 | 7 | -7 |
Since -7 is the coefficient of the middle term, x2 - 7x + 12 = (x - 3)(x - 4)
}}} {{{ visual_factor_BCform(-8,6) /// This quadratic is un-factorable. }}} {{{ visual_factor_BCform(1,-12) ///Factor completely: x2 + x - 12
First, determine all integer pairs whose product is -12 and then compute each sum.
Integer pairs whose product is -12 | 1,-12 | -1,12 | 2,-6 | -2,6 | 3,-4 | -3,4 |
Sum | -11 | 11 | -4 | 4 | -1 | 1 |
Since 1 is the coefficient of the middle term, x2 + x - 12 = (x - 3)(x + 4)
}}} {{{ visual_factor_BCform(2,1) ///Factor completely: x2 + 2x + 1
First, determine all integer pairs whose product is 1 and then compute each sum.
Integer pairs whose product is 1 | 1,1 | -1,-1 |
Sum | 2 | -2 |
Since 2 is the coefficient of the middle term, x2 + 2x + 1 = (x + 1)2
}}} {{{ visual_factor_BCform(3,-40) ///Factor completely: x2 + 3x - 40
First, determine all integer pairs whose product is -40 and then compute each sum.
Integer pairs whose product is -40 | 1,-40 | -1,40 | 2,-20 | -2,20 | 4,-10 | -4,10 | 5,-8 | -5,8 |
Sum | -39 | 39 | -18 | 18 | -6 | 6 | -3 | 3 |
Since 3 is the coefficient of the middle term, x2 + 3x - 40 = (x - 5)(x + 8)
}}} {{{ visual_factor_BCform(34,-287) ///Factor completely: x2 + 34x - 287
First, determine all integer pairs whose product is -287 and then compute each sum.
Integer pairs whose product is -287 | 1,-287 | -1,287 | 7,-41 | -7,41 |
Sum | -286 | 286 | -34 | 34 |
Since 34 is the coefficient of the middle term, x2 + 34x - 287 = (x - 7)(x + 41)
}}} {{{ visual_factor_BCform(-4,4) ///Factor completely: x2 - 4x + 4
First, determine all integer pairs whose product is 4 and then compute each sum.
Integer pairs whose product is 4 | 1,4 | -1,-4 | 2,2 | -2,-2 |
Sum | 5 | -5 | 4 | -4 |
Since -4 is the coefficient of the middle term, x2 - 4x + 4 = (x - 2)2
}}} {{{ visual_factor_BCform(4,4) ///Factor completely: x2 + 4x + 4
First, determine all integer pairs whose product is 4 and then compute each sum.
Integer pairs whose product is 4 | 1,4 | -1,-4 | 2,2 | -2,-2 |
Sum | 5 | -5 | 4 | -4 |
Since 4 is the coefficient of the middle term, x2 + 4x + 4 = (x + 2)2
}}} {{{ visual_factor_BCform(-2,1) ///Factor completely: x2 - 2x + 1
First, determine all integer pairs whose product is 1 and then compute each sum.
Integer pairs whose product is 1 | 1,1 | -1,-1 |
Sum | 2 | -2 |
Since -2 is the coefficient of the middle term, x2 - 2x + 1 = (x - 1)2
}}} {{{ visual_factor_BCform(-10,25) ///Factor completely: x2 - 10x + 25
First, determine all integer pairs whose product is 25 and then compute each sum.
Integer pairs whose product is 25 | 1,25 | -1,-25 | 5,5 | -5,-5 |
Sum | 26 | -26 | 10 | -10 |
Since -10 is the coefficient of the middle term, x2 - 10x + 25 = (x - 5)2
}}} {{{ }}} {{{ visual_factor_BCform(10,25) ///Factor completely: x2 + 10x + 25
First, determine all integer pairs whose product is 25 and then compute each sum.
Integer pairs whose product is 25 | 1,25 | -1,-25 | 5,5 | -5,-5 |
Sum | 26 | -26 | 10 | -10 |
Since 10 is the coefficient of the middle term, x2 + 10x + 25 = (x + 5)2
}}} {{{ visual_factor_BCform(2,1) ///Factor completely: x2 + 2x + 1
First, determine all integer pairs whose product is 1 and then compute each sum.
Integer pairs whose product is 1 | 1,1 | -1,-1 |
Sum | 2 | -2 |
Since 2 is the coefficient of the middle term, x2 + 2x + 1 = (x + 1)2
}}} {{{ visual_factor_BCform(5,6) ///Factor completely: x2 + 5x + 6
First, determine all integer pairs whose product is 6 and then compute each sum.
Integer pairs whose product is 6 | 1,6 | -1,-6 | 2,3 | -2,-3 |
Sum | 7 | -7 | 5 | -5 |
Since 5 is the coefficient of the middle term, x2 + 5x + 6 = (x + 2)(x + 3)
}}} {{{ visual_factor_BCform(6,8) ///Factor completely: x2 + 6x + 8
First, determine all integer pairs whose product is 8 and then compute each sum.
Integer pairs whose product is 8 | 1,8 | -1,-8 | 2,4 | -2,-4 |
Sum | 9 | -9 | 6 | -6 |
Since 6 is the coefficient of the middle term, x2 + 6x + 8 = (x + 2)(x + 4)
}}} {{{ visual_factor_BCform(10,16) ///Factor completely: x2 + 10x + 16
First, determine all integer pairs whose product is 16 and then compute each sum.
Integer pairs whose product is 16 | 1,16 | -1,-16 | 2,8 | -2,-8 | 4,4 | -4,-4 |
Sum | 17 | -17 | 10 | -10 | 8 | -8 |
Since 10 is the coefficient of the middle term, x2 + 10x + 16 = (x + 2)(x + 8)
}}} {{{ visual_factor_BCform(7,6) ///Factor completely: x2 + 7x + 6
First, determine all integer pairs whose product is 6 and then compute each sum.
Integer pairs whose product is 6 | 1,6 | -1,-6 | 2,3 | -2,-3 |
Sum | 7 | -7 | 5 | -5 |
Since 7 is the coefficient of the middle term, x2 + 7x + 6 = (x + 1)(x + 6)
}}} {{{ visual_factor_BCform(9,8) ///Factor completely: x2 + 9x + 8
First, determine all integer pairs whose product is 8 and then compute each sum.
Integer pairs whose product is 8 | 1,8 | -1,-8 | 2,4 | -2,-4 |
Sum | 9 | -9 | 6 | -6 |
Since 9 is the coefficient of the middle term, x2 + 9x + 8 = (x + 1)(x + 8)
}}} {{{ visual_factor_BCform(7,10) ///Factor completely: x2 + 7x + 10
First, determine all integer pairs whose product is 10 and then compute each sum.
Integer pairs whose product is 10 | 1,10 | -1,-10 | 2,5 | -2,-5 |
Sum | 11 | -11 | 7 | -7 |
Since 7 is the coefficient of the middle term, x2 + 7x + 10 = (x + 2)(x + 5)
}}} {{{ visual_factor_BCform(11,10) ///Factor completely: x2 + 11x + 10
First, determine all integer pairs whose product is 10 and then compute each sum.
Integer pairs whose product is 10 | 1,10 | -1,-10 | 2,5 | -2,-5 |
Sum | 11 | -11 | 7 | -7 |
Since 11 is the coefficient of the middle term, x2 + 11x + 10 = (x + 1)(x + 10)
}}} {{{ visual_factor_BCform(-10,16) ///Factor completely: x2 - 10x + 16
First, determine all integer pairs whose product is 16 and then compute each sum.
Integer pairs whose product is 16 | 1,16 | -1,-16 | 2,8 | -2,-8 | 4,4 | -4,-4 |
Sum | 17 | -17 | 10 | -10 | 8 | -8 |
Since -10 is the coefficient of the middle term, x2 - 10x + 16 = (x - 2)(x - 8)
}}} {{{ visual_factor_BCform(2,8) /// This quadratic is un-factorable. }}} {{{ visual_factor_BCform(-17,16) ///Factor completely: x2 - 17x + 16
First, determine all integer pairs whose product is 16 and then compute each sum.
Integer pairs whose product is 16 | 1,16 | -1,-16 | 2,8 | -2,-8 | 4,4 | -4,-4 |
Sum | 17 | -17 | 10 | -10 | 8 | -8 |
Since -17 is the coefficient of the middle term, x2 - 17x + 16 = (x - 1)(x - 16)
}}} {{{ visual_factor_BCform(-7,-8) ///Factor completely: x2 - 7x - 8
First, determine all integer pairs whose product is -8 and then compute each sum.
Integer pairs whose product is -8 | 1,-8 | -1,8 | 2,-4 | -2,4 |
Sum | -7 | 7 | -2 | 2 |
Since -7 is the coefficient of the middle term, x2 - 7x - 8 = (x + 1)(x - 8)
}}} {{{ visual_factor_BCform(-2,-8) ///Factor completely: x2 - 2x - 8
First, determine all integer pairs whose product is -8 and then compute each sum.
Integer pairs whose product is -8 | 1,-8 | -1,8 | 2,-4 | -2,4 |
Sum | -7 | 7 | -2 | 2 |
Since -2 is the coefficient of the middle term, x2 - 2x - 8 = (x + 2)(x - 4)
}}} {{{ visual_factor_BCform(7,-8) ///Factor completely: x2 + 7x - 8
First, determine all integer pairs whose product is -8 and then compute each sum.
Integer pairs whose product is -8 | 1,-8 | -1,8 | 2,-4 | -2,4 |
Sum | -7 | 7 | -2 | 2 |
Since 7 is the coefficient of the middle term, x2 + 7x - 8 = (x - 1)(x + 8)
}}} {{{ visual_factor_BCform(2,-8) ///Factor completely: x2 + 2x - 8
First, determine all integer pairs whose product is -8 and then compute each sum.
Integer pairs whose product is -8 | 1,-8 | -1,8 | 2,-4 | -2,4 |
Sum | -7 | 7 | -2 | 2 |
Since 2 is the coefficient of the middle term, x2 + 2x - 8 = (x - 2)(x + 4)
}}} {{{ visual_factor_BCform(-16,-80) ///Factor completely: x2 - 16x - 80
First, determine all integer pairs whose product is -80 and then compute each sum.
Integer pairs whose product is -80 | 1,-80 | -1,80 | 2,-40 | -2,40 | 4,-20 | -4,20 | 5,-16 | -5,16 | 8,-10 | -8,10 |
Sum | -79 | 79 | -38 | 38 | -16 | 16 | -11 | 11 | -2 | 2 |
Since -16 is the coefficient of the middle term, x2 - 16x - 80 = (x + 4)(x - 20)
}}} {{{ visual_factor_BCform(4,-32) ///Factor completely: x2 + 4x - 32
First, determine all integer pairs whose product is -32 and then compute each sum.
Integer pairs whose product is -32 | 1,-32 | -1,32 | 2,-16 | -2,16 | 4,-8 | -4,8 |
Sum | -31 | 31 | -14 | 14 | -4 | 4 |
Since 4 is the coefficient of the middle term, x2 + 4x - 32 = (x - 4)(x + 8)
}}} {{{ visual_factor_BCform(9,18) ///Factor completely: x2 + 9x + 18
First, determine all integer pairs whose product is 18 and then compute each sum.
Integer pairs whose product is 18 | 1,18 | -1,-18 | 2,9 | -2,-9 | 3,6 | -3,-6 |
Sum | 19 | -19 | 11 | -11 | 9 | -9 |
Since 9 is the coefficient of the middle term, x2 + 9x + 18 = (x + 3)(x + 6)
}}} {{{ visual_factor_BCform(17,60) ///Factor completely: x2 + 17x + 60
First, determine all integer pairs whose product is 60 and then compute each sum.
Integer pairs whose product is 60 | 1,60 | -1,-60 | 2,30 | -2,-30 | 3,20 | -3,-20 | 4,15 | -4,-15 | 5,12 | -5,-12 | 6,10 | -6,-10 |
Sum | 61 | -61 | 32 | -32 | 23 | -23 | 19 | -19 | 17 | -17 | 16 | -16 |
Since 17 is the coefficient of the middle term, x2 + 17x + 60 = (x + 5)(x + 12)
}}} {{{ visual_factor_BCform(20,36) ///Factor completely: x2 + 20x + 36
First, determine all integer pairs whose product is 36 and then compute each sum.
Integer pairs whose product is 36 | 1,36 | -1,-36 | 2,18 | -2,-18 | 3,12 | -3,-12 | 4,9 | -4,-9 | 6,6 | -6,-6 |
Sum | 37 | -37 | 20 | -20 | 15 | -15 | 13 | -13 | 12 | -12 |
Since 20 is the coefficient of the middle term, x2 + 20x + 36 = (x + 2)(x + 18)
}}} {{{ visual_factor_BCform(10,-3*13) ///Factor completely: x2 + 10x - 39
First, determine all integer pairs whose product is -39 and then compute each sum.
Integer pairs whose product is -39 | 1,-39 | -1,39 | 3,-13 | -3,13 |
Sum | -38 | 38 | -10 | 10 |
Since 10 is the coefficient of the middle term, x2 + 10x - 39 = (x - 3)(x + 13)
}}} {{{ }}}