Question

1) What is a term in an algebraic expression or equation? In other words, how would you distinguish a term of an expression from something else (e.g., a factor)? 2) What does a monomial look like? And, what is a polynomial? Is it true that a monomial is just a single term of a polynomial? 3) What is a factor of a polynomial? Can you define it using the notion of a term or monomial of a polynomial? 4) What is the GCF (greatest common factor) or GCD (greatest common divisor) of a polynomial? 5) Find the GCF of the following polynomial p(x) = 2x*y– 2x²y+ 12x’y and then completely factor this polynomial using the guessing method.

Answer 1

1)

An expression or equation is made up of terms seperated by + or - sign

For example

4x + 5

In this expression 4x and 5 are terms

2)

Monomial is an algebraic expression consisting of one term

Whereas polynomial consists of multiple terms

Polynomial is basically made up of monomials

Its true that monomial is just a single term of polynomial

3)

A factor of polynomial is a term or expression that divides polynomial completely

For example

In, 2x + 4

Factor of polynomial is 2

As 2 divides 2x + 4 completely

4)

GCF is the greatest common factor of any polynomial

For example

5x^2 + 5x

In this polynomial

5x is the common factor

So 5x is GCF

5)

p(x) = 2x^4y - 2x^3y + 12x^2y

GCF is 2x^2y

Taking out the GCF to factor the polynomial

2x^2y ( x^2 - x + 6 )