Use the given zero to find the remaining complex zeros of the polynomial function and write the polynomial as a product of linear factors.

f(x)=x^3+8x^2+6x-52; zero:2

(x - 2)(x - 5 + 2i)(x - 5 - 2i)

Step-by-step explanation:

If one zero is 2, then one factor is (x - 2).

Use synthetic division here.  Taking the coefficients 1, 8, 6 and -52, divide 2 into them:

2    /  1      8      6     -52

                2     20     52

          1     10     26     0

Because the remainder is zero, we know that 2 is a root and (x - 2) is a factor, and that the coefficients of the quadratic quotient are 1, 10 and 26.

The discriminant is thus b^2 - 4ac, or 10^2 - 4(1)(26), or  100 - 104, or -4.

Because the discriminant is negative, we know that there will be two factors which themselves are complex conjugates.  One such factor is

      10 ± √-4         10 ± 2i

x = =

             2                   2

The complex zeros are thus x = 5 ± 2i.

The corresponding factors are (x - 5 + 2i) and (x - 5 - 2i)

and so the polynomial is

(x - 2)(x - 5 + 2i)(x - 5 - 2i)

1/3

step-by-step explanation:

to find this, you can divide 12 by 4 which is 3 or you can multiply 4 until you reach 12 (4x3=12). both should give you 3, meaning theres three times less bananas than there are oranges.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)