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

step-by-step explanation:

(1,4) is on graph of f(x)

f(1) = 4

so 1/4 f(x)

1/4 f(1)

1/4. ×4

1

so point for function 1/4. f(x) is (1,1)