Question

Which partial form corresponds to \[\frac{\mathrm{p}x^{2}+\mathrm{q}x+\mathrm{r}}{(x-\mathrm{a})(x-\mathrm{b})(x-\mathrm{c})}\]?

Options

• \[\frac{\mathrm{A}}{x-\mathrm{a}}+\frac{\mathrm{B}}{x-\mathrm{b}}+\frac{\mathrm{C}}{x-\mathrm{c}}\]

• \[\frac{\mathrm{A}}{(x-\mathrm{a})^{2}}+\frac{\mathrm{B}}{x-\mathrm{b}}+\frac{\mathrm{C}}{x-\mathrm{c}}\]

• \[\frac{\mathrm{A}x+\mathrm{B}}{x-\mathrm{a}}+\frac{\mathrm{C}}{x-\mathrm{b}}\]

• \[\frac{\mathrm{A}}{x^{2}+\mathrm{b}x+\mathrm{c}}\]

Answer 1

There are three distinct non-repeated linear factors. Therefore, the partial form requires the three constant-numerator terms shown.