Q. \(\,x^2 + x\,\)
Answer
We factor the polynomial \(x^2+x\) by taking out the greatest common factor \(x\):
\[
x^2+x=x(x+1)
\]
Final result: \(x(x+1)\)
Detailed Explanation
We want to simplify the expression \(x^2 + x\) (often written as a polynomial expression). A common and useful thing to do with a quadratic like this is to factor it, if possible.
Step 1: Identify common factors.
The expression is \(x^2 + x\). Both terms contain \(x\) as a factor.
So we can take out the greatest common factor \(x\):
\[
x^2 + x = x(x + 1)
\]
Step 2: Write the factored form.
After factoring, the expression becomes:
\[
x^2 + x = x(x + 1)
\]
Final Answer:
\[
x^2 + x = x(x + 1)
\]
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Algebra FAQ
Factor \(x^2+x\).
\(\,x^2+x=x(x+1)\).
Solve \(x^2+x=0\).
\(\,x(x+1)=0\Rightarrow x=0\) or \(x=-1\).
Complete the square for \(x^2+x\).
\(x^2+x=\left(x+\frac{1}{2}\right)^2-\frac{1}{4}\).
Find the derivative of \(x^2+x\).
\(\,\frac{d}{dx}(x^2+x)=2x+1\).
Find the minimum value of \(x^2+x\) and where it occurs.
Parabola opens up; vertex at \(x=-\frac{1}{2}\). Minimum value is \(-\frac{1}{4}\).
Evaluate \(x^2+x\) at \(x=3\).
\(3^2+3=9+3=12\).
What is the discriminant of \(x^2+x=0\)?
For \(x^2+1x+0\), \(a=1,b=1,c=0\). Discriminant \(b^2-4ac=1\).
Use these tools to practice x²+x.
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