Mathematics

When you divide a polynomial by $x^2 - 1$, the remainder must be a linear polynomial (degree less than 2). The key insight is that the original polynomial can be written as $q(x)(x^2 - 1) + (7x + 9)$, where $q(x)$ is the quotient. By expanding and comparing coefficients of the original polynomial, you can set up equations to solve for the unknown constants $c$ and $d$.

When you divide a polynomial by $x^2 - 1$, the remainder must be a linear polynomial (degree less than 2). The key insight is that the original polynomial can be written as $q(x)(x^2 - 1) + (7x + 9)$, where $q(x)$ is the quotient. By expanding and comparing coefficients of the original polynomial, you can set up equations to solve for the unknown constants $c$ and $d$.