Determine a equation (in factored form) a cubic with zeros of 3, 2, and -1 and passes through the point(-2,40)

Question

so far i have (x-3)(x-2)(x+1). However, i do not know how to fit in the second part of the question.

Answer 1

Put y=A(x-3)(x-2)(x+1) where A is some constant. Now substitute x=-2 and y=40 to get A=-2.
So the equation is:

y=-2(x-3)(x-2)(x+1)

Answer 2

Plug in -2:

(-2-3)(-2-2)(-2+1) = (-5)(-4)(-1) = -20

You want the value of this equation to be 40 at -2. It is currently -20. Thus, you must multiply it by 40/(-20) or -2. So you have:

-2(x-3)(x-2)(x-1)

And you are done. Note that the reason we multiply by a constant instead of using some other operation to change the value of the polynomial (such as adding 60) is that any other operation would change the zeros of the polynomial.

Answer 3

The key to the solution for you is to realize that their are an infinite number of solutions for the first part, all being given by a non-zero constant multiple of your answer:
A(x-2)(x-3)(x+1)

So all you need is fit your function to the condition by equating the value of the function at -2 to 40.

A(-2-2)(-2-3)(-2+1) = 40 or -20A = 40

So A = -2

So the equation is -2(x-3)(x-2)(x+1)

Answer 4

First locate the slope of the line. The slope is given by using upward thrust/run. additionally commonplace as. m= (y1 - y2) / (x1 - x2) So the slope is: m = (a million - [-2] ) / (3 - [-a million]) = 3 / 4 via fact the slope is 3/4 you are able to placed it into an equation like this: y = mx + C y = (3/4)x + C Now plug in one among your factors to be certain what C is. a million = (3/4)(3) + C a million = (9/4) + C (4/4) - (9/4) = C -5/4 = C So C is comparable to -5/4. So your very final equation is: y = (3/4)x - (5/4)

Answer 5

(x - 3)(x - 2)(x + 1)

f(-2) = (-2 - 3)(-2 - 2)(-2 + 1)
f(-2) = (-5)(-4)(-1)
f(-2) = (20 * -1) = -20

40/-20 = -2

f(x) = -2(x - 3)(x - 2)(x + 1)
f(x) = -2(x^2 - 2x - 3x + 6)(x + 1)
f(x) = -2(x^2 - 5x + 6)(x + 1)
f(x) = -2(x^3 + x^2 - 5x^2 - 5x + 6x + 6)
f(x) = -2(x^3 - 4x^2 + x + 6)

ANS : f(x) = -2x^3 + 8x^2 - 2x - 12

if you plug in -2 for x, you will get it to equal 40

Answer 6

y = (x-3)(x-2)(x+1)

if x = -2 then y = -5 * -4 * -1 = - 20 , but we want 40

40 / (-20) = -2

so let y = -2(x-3)(x-2)(x+1)