If the polynomial ax2+bx+5 leaves a remainder 3 when divided by x−1, and a remainder 2 when divided by x+1, then 2b−4a equals _____________.

Question

Accepted Answer

Use Remainder Theorem: For polynomial f(x), remainder on division by (x−a) is f(a).Let f(1)=3 and f(−1)=2, giving a+b+5=3 and a−b+5=2.Solving: a+b=−2, a−b=−3 so 2a=−5, a=−5/2, b=1/2.2b−4a=1−(−10)=11