If (p(x)=27+6x) and (q(x)=9x-6), when will (p(x)) and (q(x)) be equal?

Correct answer: \(x=11\)

For the two polynomials to be equal, set \(p(x)=q(x)\): \(27+6x=9x-6\). Subtracting \(6x\) from both sides gives \(27=3x-6\). Adding 6 to both sides gives \(33=3x\), so \(x=11\). At \(x=10\), the values of the two polynomials are not equal. Exam tip: To find where two expressions are equal, equate them first and solve the resulting linear equation.