Question

Plz help!

Answer 1

Step-by-step explanation:

let's look at the last line :

x³ + 8x - 3 = Ax³ +5Ax + Bx² + 5B + Cx + D

since we find A, B, C, and D by simply comparing the factors of the various terms in x (or constants) in both sides of the equation, we need to combine a few terms on the right hand side (so that we have one term per x exponent grade).

x³ + 8x - 3 = Ax³ + (5A + C)x + Bx² + (5B + D)

by comparing now both sides, to make both sides truly equal, the factors have to be equal.

A = 1 (the same as for x³ on the left hand side).

B = 0 (a we have no x² on the left side).

5A + C = 8 (a 8 is the factor of x in the left side).

5×1 + C = 8

5 + C = 8

C = 3

5B + D = -3 (as the constant term is -3 on the left side).

5×0 + D = -3

D = -3

so, the 4th answer option is correct.