Factoring x^2+2x
In algebra, factoring is the process of writing a polynomial expression as the product of two or more smaller expressions. This can be done by finding common factors, using the sum-product pattern, or by grouping.
The expression x^2+2x can be factored by using the sum-product pattern. The sum-product pattern states that the product of two numbers is equal to the sum of their products with their negatives. In this case, the two numbers are x and 2. The product of these numbers is 2x. The sum of their products with their negatives is x^2-4x+2x. This simplifies to x^2-2x.
Therefore, the factored expression of x^2+2x is (x-2)x.
Related questions
- What is the factored expression of x^2-2x?
- How do you factor x^2+2x?
- What is the quadratic formula?
Answers
- The factored expression of x^2-2x is also (x-2)x.
- To factor x^2+2x, you can use the sum-product pattern, the grouping method, or the quadratic formula.
- The quadratic formula is a formula that can be used to solve quadratic equations. It is given by the following equation:
x = (-b ± √(b^2 - 4ac)) / 2a where a, b, and c are the coefficients of the quadratic equation.
Discussion
Factoring is a useful skill in algebra. It can be used to simplify expressions, solve equations, and understand the relationship between different expressions.
In the case of x^2+2x, factoring the expression can be helpful for understanding how it can be solved. The factored expression shows that x^2+2x can be written as the product of two linear expressions. This means that the equation x^2+2x=0 can be solved by setting each of the linear expressions equal to 0.
In other words, the equation x^2+2x=0 has two solutions:
x-2 = 0 x = 2 and
x = 0 Therefore, the factored expression of x^2+2x can be used to solve the equation x^2+2x=0.
