WAEC Further Mathematics 2015 Paper

Concept:Compare the coefficients of like terms after expanding both sides of the given equation.Explanation:Start with the given equation: $x^{2} + 4x + k = (x + r)^{2} + 1$.Expand the right-hand side using $(x + r)^{2} = x^{2} + 2rx + r^{2}$.Thus, the equation becomes $x^{2} + 4x + k = x^{2} + 2rx + r^{2} + 1$.Since both sides are identical polynomials, their corresponding coefficients must be equal.Compare the coefficient of $x$: $4 = 2r$, so $r = 2$.Compare the constant terms: $k = r^{2} + 1$.Substitute $r = 2$: $k = (2)^{2} + 1 = 4 + 1 = 5$.Therefore, $k = 5$ and $r = 2$.Answer:$k = 5$, $r = 2$ (Option B).