Factor the polynomial given that f(k) = 0

x^3 - 5x^2 - 2x + 24; k = -2

i'm hoping somebody can explain how to figure out one of these problems.

The following polynomial can be factorized as,

f(x) =

Step-by-step explanation:

It is given that at x = -2, the value of polynomial is zero, thus, by factor theorm,  

(x+2) is the factor of the above polynomial.

By dividing the given polynomial by (x+2), we get,

F(x) =

This can be further simplified as,

=

= =

Thus the polynomial becomes,

f(x) =

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

the least value out of the data shown is 5, maybe if you post a picture with it i could a little more.

step-by-step explanation: