Question

the polynomials ax^3+3x^2-3 and 2x^3-5x+a when divided by (x-4) leaves the remainder m and n respectively. find a if m+n=0

Answer 1

let f(x)=ax³+3x²-3 and g(x)=2x³-5x+a

by remainder theoram if f(x) is devided by (x-4) then remainder f(4) or m
f(x)=ax³+3x²-3
f(4)=a(4)³+3(4)²-3
=64a+48-3
=64a+45
again by remainder theoram if g(x) is decided by (x-4) then remainder =g(4) or n
g(x)=2x³-5x+a
=2(4)³-5(4)+a
=128-20+a
=118+a
given,
$m + n = 0$
64a+45+118+a=0
65a+163=0
65a=-163
a=-163/65
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