1. Greatest Common Factor: The Greatest Common Factor (GCF) is the largest number which can divide a set of numbers simultaneously.
  2. You know you have reached the GCF when there is no other number that can divide the set of numbers you are working with simultaneously.
  3. Polynomials: A polynomial refers to an expression with two or more terms.

Examples of polynomials and their GCF:

  • 4x4 + 2x2 + x = x(4x3 + 2x + 1)
  • y5 + 6y3 + y2 = y2(y3 + 6y + 1)
  • z4 + 2z3 + z2 + 7z = z(z3 + 2z2 + z + 7)
  1. Rational Expression: Rational expression refers to the quotient of two polynomials.
  2. Explanation of rational expression: Rational expressions in polynomials are similar to rational numbers in integers.

Examples of rational expressions and their simplified forms:

  • 4x + 8/ 4x – 8 = 4(x + 2)/ 4(x – 2) = x + 2/x – 2
  • 6z2 + 3z/ 3z2 + 3z = 3z(2z + 1)/3z(z + 3) = 2z + 1/ z + 3
Don't wait until tomorrow!

You can use our chat service now for more immediate answers. Contact us anytime to discuss the details of the order

Place an order
  1. Factoring the difference of two squares: The model used to factor the difference of two squares is as follows:

a2 – b2 = (a + b) (a – b)

  1. Factoring perfect square trinomials: The models used to factor perfect square polynomials is as follows:

a2 + 2ab + b2 = (a + b) 2 and a2 - 2ab + b2 = (a - b) 2  

  1. All of the above models make sense to me.
  2. Factoring the difference of two squares seems much easier than factoring perfect square trinomials because in factoring perfect square trinomials, you must first determine whether the expression is a perfect square trinomial. In contrast, the difference of two squares is obvious.

Examples:

  • The difference of two squares:

25x2 – 16y2 = (5x – 4y) (5x – 4y)

  • Perfect square trinomial;

x2 + 24x + 144 = (x + 12)2

Calculate the Price of Your Paper

 
-+
 

Related essays

  1. The Role of the Roman Army in Britain
  2. Negotiation and Conflict Resolution
  3. Information Request
  4. University Scholarship Personal Statement
Discount applied successfully