What would be the remainder ?

A

Step-by-step explanation:

Given (x + h) is a factor of f(x) then f(- h) = 0

Given

p(x) = x³ - 4x² + ax + 20 , with (x + 1) as a factor then

p(- 1) = (- 1)³ - 4(- 1)² - a + 20 = 0 , that is

- 1 - 4 - a + 20 = 0

15 - a = 0 ( subtract 15 from both sides )

- a = - 15 ( multiply both sides by - 1 )

a = 15 , thus

p(x) = x³ - 4x² + 15x + 20

If p(x) is divided by (x + h) then p(- h) is the remainder, so

p(- 2) = (- 2)³ - 4(- 2)² + 15(- 2) + 20 , that is

- 8 - 16 - 30 + 20 = - 34 → A

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

x is the total time in minutes for the free response

you are given number of questions as 15 - m and time per item as 8 minutes

to find x multiply the two givens together:

x = 8 * (15-m) = 8(15-m)