x3 − 4x2 + 3x + 7 divided by (x + 5)
I'm studying for a quiz but I don't understand how to do this.
Please explain. Brainliest only will be given if it includes an explanation.
I will report you if you give some random answer just for the points, don't test me.

Step-by-step explanation:

x³ - 4x² + 3x + 7

= (x + 5)(Ax² + Bx + C) + D

= Ax³ + (B + 5A)x²+ (C + 5B)x + (D + 5C).

By Comparing Coefficients, we have

A = 1

B + 5A = -4

C + 5B = 3

D + 5C = 7

Solving them, we have A = 1, B = -9, C = 48 and D = -233.

Hence x³ - 4x² + 3x + 7 = (x + 5)(x² - 9x + 48) - 233.

a and c

for infinitely many solutions we require both left and right sides to be equal

distribute and simplify

a

14 - 8x = 20 - 8x - 6 = 14 - 8x ← both sides equal so infinite solutions

b

6x - 54 = 6x - 54 + x = 7x - 54 ← not equal

c

4x + 16 = 4x + 10 + 6 = 4x + 16 ← both sides equal so infinite solutions

d

5x - 40 + 10 = 5x + 10

5x - 30 = 5x + 10 ← not equal