(x + 1)(x + 5)
(x + 1)(x + 5)
32
Suppose the number is x. Then x + 5/x = 6 Multiplying throughout by x, x2+5 = 6x or x2 - 6x + 5 = 0 which can be factorised into (x-1)*(x-5)=0 So x = 1 (and 5 times its reciprocal is 5) or x = 5 (and 5 times its reciprocal is 1).
6x - 5 -5 = 0 6x -10 = 0 +10=+10 6x=10 x= about 1.4
x2 - 6x + 5 = (x - 1)(x - 5)
x2 + 6x + 5 can be factored into (x+1) (x+5)
x2 + 6x - 5 is a quadratic expression that can not be factored.
The following equations are all equivalent to y = x2 - 6x + 14:y - 5 = (x - 3)22y = 2x2 - 12x + 28± √(y - 5) = x - 3y = [x4 - 4(3x3 + [4x]2 - 42x + 49)]1/2y - 5 = x2 - 6x + 92y - 5 = 2(x2 - 6x) + 23x = 3 ± √(y - 5)
(X + 5)(X + 1) FOIL this. X2 + 1X + 5X + 5 Gather terms. X2 + 6X + 5 ----------------------------those were the factors
(x + 1)(x + 5)
You don't have an equation there.
6x3+29x2-40x-42 divided by 6x+5 is x2+4x-10 remainder 8 or as x2+4x-10+8/(6x+5) If the answer is correct then the quotient multiplied by the divisor should be the same as the dividend:- (6x+5)*(x2+4x-10) + (6x+5)*8/(6x+5) Multiply term by term with (6x+5):- 6x3+5x2+24x2+20x-60x-50+8 Collect like terms:- 6x3+29x2-40x-42 which makes the answer correct.
6x - 1 = 29 => 6x = 30 => x = 5 Then x2 + x = 25 + 5 = 30
Potential respondents would be assisted by knowing the sign of the 6x element as there is no solution in integers.
x2+6x+5=0(x+1)(x+5)=0x=-1 and x=-51-6+5=0 and 25-30+5=0 so both answers work.
6x5(x2 - 6x + 3)