What is the remainder when (4x3 + 2x2 − 18x + 38) ÷ (x + 3)?
2
12
96
110

 First Option is correct.

Step-by-step explanation:

Since we have given that

We will apply the "Remainder Theorem ":

So, first we take

So, we will put x=-3 in f(x).

So, Remainder of this division is 2.

Hence, First Option is correct.

look at the picture.

1.

ef : ab = 2 : 3

gf : cb = 2 : 3

gh : cd = 2 : 3

he : da = 2 : 3

2.

∠a ≅ ∠e

∠b ≅ ∠f

∠c ≅ ∠g

∠d ≅ ∠h

3.

use pythagorean theorem:

the length of the abcd trapezoid sides:

|ab| = 3 cm

|bc| = 10 cm

|cd| = 3(3) cm = 9 cm

|da| = 8 cm

the perimeter of abcd = 3 + 10 + 9 + 8 = 30 cm

the ratio of perimeters of the tarapezoids is equal 2 : 3.

substitute:

      cross multiply

      divide both sides by 3