# Tag Archives: polynomial

## Third Root of Equation

Two of the roots of the equation are and . Find the third root of the equation. Source: NCTM Mathematics Teacher, August 2006 Solution Let be the third root of the equation. We write the equation in factored form Multiply … Continue reading

## Remainder

What is the remainder when is divided by ? Source: NCTM Mathematics Teacher, November 2006 SOLUTION If a polynomial is divided by a polynomial , there exists a quotient polynomial and a remainder polynomial such that with . Though tedious … Continue reading

## Factors of Polynomial

How many different polynomials of the form with rational coefficients are factors of the polynomial ? Source: NCTM Mathematics Teacher, February 2006 SOLUTION Putting all the factors together into Eq. There are ways to get a product of degree from the factors … Continue reading

## Algebraic Expansion

If you expand the polynomial , the resulting polynomial has three terms whose coefficients are 1, 2, and 1. Find the sum of the coefficients of the terms in the expansion of . Source: mathcontest.olemiss.edu 5/5/2008 SOLUTION We use the “area” model … Continue reading

## 615

You are given two positive integers, , such that . Find the sum of x and y. Source: mathcontest.olemisss.edu 11/30/2009 SOLUTION Since the first factor is positive, the second factor must be negative. Prime factorization: . There are three possibilities: … Continue reading

## X, Y, and Z

You are given real numbers where . Find the value of . Source: mathcontest.olemiss.edu 2/21/2011 SOLUTION Finding Solving the equation yields . . Finding Solving the equation yields . . Sum of Subtracting from both sides of the above equation yields Right-hand … Continue reading

## 2003 Expansion

When the following expression is expanded, what will be the coefficient of ? Source: mathcontest.olemiss.edu 7/7/2008 SOLUTION STEP 1 Product of two factors: . Let be the 9 coefficients, then we have . Let . The coefficients follow the pattern … Continue reading