What is x squared plus x
The Correct answer and Explanation is:
The expression “x squared plus x” can be written as:
x2+xx^2 + xx2+x
This is a polynomial expression where x2x^2×2 is a quadratic term and xxx is a linear term. The two terms are added together, but they cannot be simplified further because they are not like terms (like terms have the same variable raised to the same power). However, this expression can be factored or used in various ways depending on the context.
Factoring
One common operation with this expression is factoring. To factor x2+xx^2 + xx2+x, you can factor out the common factor of xxx. This would look like:x2+x=x(x+1)x^2 + x = x(x + 1)x2+x=x(x+1)
This shows that the expression is the product of xxx and (x+1)(x + 1)(x+1). This factored form can be useful in solving equations or simplifying problems.
Solving Equations
If you set x2+xx^2 + xx2+x equal to 0 (to solve for xxx):x2+x=0x^2 + x = 0x2+x=0
You can solve this by factoring:x(x+1)=0x(x + 1) = 0x(x+1)=0
This gives two solutions:x=0orx+1=0⇒x=−1x = 0 \quad \text{or} \quad x + 1 = 0 \quad \Rightarrow \quad x = -1x=0orx+1=0⇒x=−1
So, the solutions to the equation x2+x=0x^2 + x = 0x2+x=0 are x=0x = 0x=0 and x=−1x = -1x=−1.
Applications
Expressions like x2+xx^2 + xx2+x appear frequently in algebra and calculus. For example, in quadratic equations, this type of expression might represent a mathematical model for a physical system, or it could appear in optimization problems. In calculus, it might arise when finding derivatives or integrals.
Conclusion
The expression x2+xx^2 + xx2+x is a quadratic expression. It can be factored as x(x+1)x(x + 1)x(x+1) and solved for x=0x = 0x=0 or x=−1x = -1x=−1 when set equal to 0. It plays an important role in various areas of algebra and calculus, particularly in solving equations and modeling real-world scenarios.