If fx = 2 x power 4 minus 2 x ki power 3 + 3 x power 2 minus a x + b when divided by x minus 1 and x + 2 leaf 5 and 19 respectively as remainders determine the remainder when f x is divided by x minus 2
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f(x)=x^4–2x^3+3x^2-ax+b.
Put x=1
5=1–2+3-a+b
3=-a+b
a-b=-3………..(1)
put x=-1
19=1+2+3+a+b
a +b=13…………..(2)
On solving eq.(1) & (2) a=5 and b= 8
Therefore f(x)=x^4–2x^3+3x^2–5x+8
Put x=3
Remainder=3^4–2.3^3+3.3^2–5.3+8
=81–54+27–15+8
=116–69
=47 , Answer:
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