Given one factor of the polynomial, factor the polynomial completely.

f(x) = x^3 - 4x^2 - 7x + 10; x - 5

The factors are (x  - 1)(x - 5)(x + 2).

Step-by-step explanation:

Long division:

x - 5 )x^3 - 4x^2 - 7x + 10( x^2 + x - 2 < Quotient.

        x^3 - 5x^2

                   x^2 - 7x

                    x^2 - 5x

                           - 2x + 10

                            -2x + 10

x^ 2 + x - 2 = (x + 2)(x - 1).

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 answers are in the images, i received 100% on this assignment. hope this !