Remainder Theorem Practice

MathSci Problems Remainder Theorem Practice Questions What is the remainder of x28−2×5+3x+1 ? 2. Find the value of k so that (x-3) is a factor of: x4+kx2+9x−27. Solutions 1) By the Remainder Theorem, remainder on division by x+1x+1 is P(−1)P(-1) : (−1)28−2(−1)5+3=1+2+3=6.(-1)^{28}-2(-1)^5+3=1+2+3=6. 2) x−3x-3 is a factor iff P(3)=0P(3)=0 : 34+k⋅32+9⋅3−27=81+9k+27−27=81+9k.3^4+kcdot 3^2+9cdot 3-27=81+9k+27-27=81+9k. Set 81+9k=0⇒k=−981+9k=0Rightarrow k=-9 […]