What is the difference between factoring and completely factoring

This quadratic is not a perfect square. However, it is possible to write the original quadratic as the sum of this square and a constant:. Privacy Policy. Skip to main content. Quadratic Functions and Factoring. Search for:. Learning Objectives Use the factors of a quadratic equation to solve it without using the quadratic formula. Key Takeaways Key Points A quadratic equation is a polynomial equation of the second degree.

One way to solve a quadratic equation is to factor the polynomial. This is essentially the reverse process of multiplying out two binomials with the FOIL method. You can check whether your proposed solutions are actual solutions by plugging them back in to the equation to see if they satisfy the equation. Key Terms factor : To find all the mathematical objects that divide a mathematical object evenly. Learning Objectives Determine whether a quadratic equation is a perfect square and factor it accordingly if it is.

Key Takeaways Key Points Some quadratics, known as perfect squares, can be factored into two equal binomials. Perfect square quadratics have only one root. Learning Objectives Determine whether a quadratic equation is a difference of squares and factor it accordingly if it is. Key Terms square : The second power of a number, value, term or expression. Learning Objectives Employ techniques to see whether a general quadratic equation can be factored.

Key Takeaways Key Points Quadratic polynomials can often be factored with the trial and error method The first step in factoring is often to look for factors of the first and last terms. Our goal is to choose the proper combination of factors for the first and last terms such that they yield the middle term. Key Terms coefficient : a constant by which an algebraic term is multiplied. Learning Objectives Solve for the zeros of a quadratic function by completing the square.

No matter how naturally gifted one is at Mathematics, an incomplete or incorrect understanding of mathematical terms can still lead to failure. Most problems in algebra, geometry, and trigonometry can be solved if one knows how to manipulate formulas, at the same time knowing how to define and differentiate between mathematical terms. Expanding and factoring are two commonly used terms in Mathematics. However, not everyone can tell the difference between them.

Most people would simply say that both terms have something to do with removing or adding parentheses in an algebraic equation. In order to know the difference between the two terms, let us utilize the two equations. The first equation would be expanded, while the second would be factored out. How does one expand the equation: 2 3c-2? First, take note of the parentheses present in the equation. Expanding the equation means removing the parentheses.

In order to derive a parentheses-free equation, one simply multiplies the value outside the value, which is 2, to each of the values inside the parentheses. This means that 2 is multiplied to 3c, and 2 is also multiplied to The resulting equation would be 6c Since the equation has no more parentheses, it is said to be completely expanded.

If expanding means removing parentheses, then factoring out is the opposite, because it means adding parentheses to an equation. First, one takes into consideration the common variable between the two values, which is x.

Now that the difference between the two terms has been explained, one understands how important it is to know the exact definition of mathematical terms. Knowing how to expand or factor out an equation helps greatly in problem solving. It also enables one to not only solve equations, but also explain objectively the difference between two mathematical terms. In order to excel at mathematics, one should have a thorough grasp of formulas and mathematical terms. Two commonly used mathematical terms, expanding and factoring, have one thing in common: they deal with either the addition or removal of parentheses in an algebraic equation.

Expanding an algebraic equation means getting rid of the parentheses. In order to remove the parentheses, the value outside the parenthesis is multiplied to each of the values inside the parentheses. On the other hand, factoring out an algebraic equation means adding parentheses to the equation.