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#### • factor cubic equation calculator

Question:I have 2 equations, I need to know the Factors and crucially, how you got them, preferably using algebraic division to answer, the first:x^3-3x^2+4 I know that one factor is (x+1) I just need the other two the Other: x^3-3x^2-x-4 any help will be much appreciated, Thanks!! preferably in the form (x-a)(x-b)(x-c) and algebreic division to form a quadratic answer, which can be expanded to this.

Answers:1) = x^3-3x^2+4 = (x^3+x^2) + ( -4x^2-4x) + (4x+4) = (x+1)(x^2+x) -4x(x+1) + 4 (x+1) = (x+1)(x^2+x-4x+4) = (x+1)(x^2 -3x +4) There are no other factors since for 2nd equation (x^2 -3x +4), (D) = b^2 - 4ac = 9-16 is less than zero 2) For second question i have used an online utility at http://id.mind.net/~zona/ezGraph/ezGraph.html So it is clear that there is only one factor for this equation too which lies between 3 & 4. It is very hard to solve a polynomial of this kind by hand. In general a program will work fine for you. Approx solution of this is x = 3.589

Question:The base of a pyramid covers an area of 13.0 acres (1acre = 43,560 square feet) and has a height of 481 feet. If the volume of a pyramid is given by the expression V = (1/3)(b)(h) where b is the area of the base and h is the height is the height, find the area in cubic meters. That's what the problem from my book. I tried the problem and got 2.5708 x 10^6 meters cubed, but I'm not sure if I'm right. Can anyone Tell me if I have one too many significant numbers in my answer or tell me if my answer is just completely wrong? Thanks in advance.

Answers:Answer --> 2.57E+6 m^3 Given in SI units: b = 52,608.73 m^3 h = 146.6088 m Using your equation: V = (1/3) * b * h V = (1/3) * (52,608.73 m^3) * (146.6088 m) V = 2,570,968 m^3 So 2.57E+6 m^3

Question:I need to find equation of a cubic (ax^3+bx^2+cx+d) with the local max (-2,5) and inflection point (0,1) given. A little help? Thanks.

Answers:Let be f(x) = ax^3+bx^2+cx+d If for x = 0 it's inflection point then x = 0 is zeros of the second derivative of f(x) the second derivative f ' ' (x) = 6ax +2b f '' (0) = 2b then b = 0 and f (0) = 1 then d = 1 Now write f (x) = ax^3 + cx+1 if f(x) has a local max (-2,5) then x = -2 it's a zero of first derivative f ' (x) = 3ax^2+c f ' (-2 ) = 12a+c = 0 now c = -12a and f (- 2) = -8a-2c+1 = 5 then -8a +24a = 4 a = 1/4 c = - 3 then f(x) = (1/4)x^3 - 3x+1

Question:A cubic equation may be expressed as ax^3 + bx^2 +cx +d = 0 or as (x - w)(x - y)(x - z) = 0 where x,y,z are roots of the equation. Use this fact to find the values of (w+y+z), (wy+wz+yz) and (wyz) in terms of a,b,c and d I have no idea where to start. Please help me!!! thanks in advance, Steve

Answers:wyz = -d //The constant term in the cubic is always the product of the constants in the factored form. wy + wz + yz = -c //This is sum of roots taken two at a time which is the negative coefficient of the x term in the cubic. w+y+z = -b //The sum of the roots is the negative coefficient of the x^2 term. Hope this helped.