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  Hello students, I would be grateful if anyone would offer me a reference for my tutoring, it is for the UNSW tutor site, link below. Thank...

Monday, April 17, 2023

Like Q12 in LG Ex1-4B - remainder theorem and simultaneous equations

Question: When a polynomial P(x) is divided by (x+2)(x4) the quotient is the polynomial Q(x) and the remainder is ax+b.  Find a,b if P(2)=3 and P(4)=2.

Solution.

Using the factor theorem we get two equations for a,b which we can solve to find a,b.

We have P(x)=(x+2)(x4)Q(x)+ax+b

Therefore

 P(2)=3=2a+b2a+b=3  (1)

and

 P(4)=2=4a+b4a+b=2  (2)


Subtract (2)-(2) gives

1=6aa=16

Then b=3+2(1/6)=223=8/3.

Conclude: a=16  and  b=83.

Remember to check my working and tell me if I made an error!! (reward!)

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