If $$x^2 + ax + b$$, when divided by $$x + 3$$, leaves a remainder of -1 and $$x^2 + bx + a$$, when divided by $$x - 3$$, leaves a remainder of 39, then $$a + b=?$$
From remainder theorem,
If polynomial is f(x) divided by the binomial (x-a) the remainder obtained f(a).
So,
f(-3) = $$x^2 + ax + b$$
$$-3^2-3a+b=-1$$
$$9-3a+b=-1$$
$$-3a+b=-10$$ -------I
Again
f(3)=$$x^2 + bx + a$$
$$3^2+3b+a=39$$
$$9+3b+a=39$$
$$3b+a=30$$ -------II
Equating I and II by multiplying I with 3
we get b= 8 and a= 6
So, a+b = 8+6= 14.
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