SAT Mathematics Practice Test 6

The right side of the equation can be multiplied using the distributive property:.Combining like terms gives ${\mathit{p}}^2{\mathit{x}}^2-{\mathit{t}}^2$.Substituting this expression for the right side of the equation gives $4{\mathit{x}}^2-9={\mathit{p}}^2{\mathit{x}}^2-{\mathit{t}}^2$ , where $\mathit{p}$ and $\mathit{t}$ are constants. This equation is true for all values of x only when $4={\mathit{p}}^2$ and $9={\mathit{t}}^2$.If $4={\mathit{p}}^2$, then $\mathit{p}=2$ or $\mathit{p}=-2$⋅Therefore, of the given answer choices, only 2 could be the value of p.
Choices B, C, and D are incorrect. For the equation to be true for all values of $\mathit{x}$, the coefficients of ${\mathit{x}}^2$on both sides of the equation must be equal; that is, $4={\mathit{p}}^2$.Therefore, the value of pcannot be 3, 4, or 9.