Stuck on Ext 1 Polynomials Question (1 Viewer)

[155the1st]

I've been doing questions from trial papers to get ready for tomorrow's test, but I can't make heads or tails of this polynomials question:

I'm pretty sure remainder theorem is needed but I don't know how to apply it to get the exact remainder.

 

[cossine]

The reminder is one degree less than the divisor. So it is in the form mx + b. Note P(X) = (x-2)*(x+3)*Q(X) + mx + b where Q(X) is the quotient

2m + b = 4 # Since the divisor = 0 when x = 2

-3m + b = 9 # Since the divisor = 0 when x = -3

5m = -5

=> m = -1

=> b = 6

 

[A1La5]

 

[155the1st]

The reminder is one degree less than the divisor. So it is in the form mx + b. Note P(X) = (x-2)*(x+3)*Q(X) + mx + b where Q(X) is the quotient

2m + b = 4 # Since the divisor = 0 when x = 2

-3m + b = 9 # Since the divisor = 0 when x = -3

5m = -5

=> m = -1

=> b = 6

View attachment 33870

Cheers to both of you! I didn't think to just use simultaneous equations