The right side of the equation can be multiplied using the distributive property:
(px+t)(px−t)=p2x2−ptx+ptx−t2
.Combining like terms gives
p2x2−t2.Substituting this expression for the right side of the equation gives
4x2−9=p2x2−t2 , where
p and
t are constants. This equation is true for all values of x only when
4=p2 and
9=t2.If
4=p2, then
p=2 or
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
x, the coefficients of
x2on both sides of the equation must be equal; that is,
4=p2.Therefore, the value of pcannot be 3, 4, or 9.