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Step 1:: To factorize the expression $x^2 + 3x$, we need to find two factors of $3x$ whose sum is $3x$ itself.
The factors of $3x$ are $x$ and $3x$.
The sum of these factors is $x + 3x = 4x$, which is not equal to the required expression $3x$. Therefore, we need to find another way to factorize the expression.
Step 2:: Notice that the expression $x^2 + 3x$ is a quadratic expression with a positive leading coefficient.
We can factorize such expressions using the formula $ax^2 + bx + c = (x - p)(x - q)$, where $p$ and $q$ are the roots of the quadratic equation $ax^2 + bx + c = 0$.
Step 3:: To find the roots of the equation $x^2 + 3x = 1$, we can divide both sides of the equation by $x$ (assuming $x
Therefore, one of the factors of the expression $x^2 + 3x$ is $x - (-3) = x + 3$.
eq 1$).
Step 4:: To find the other factor, we can divide the expression $x^2 + 3x$ by $x + 1$.
This gives us the quotient $x$.
Therefore, the other factor is $x$.
Step 5:: Hence, the factorization of the expression $x^2 + 3x$ is $(x)(x + 3)$.
Final Answer
The factorization of $x^2 + 3x$ is $(x)(x + 3)$.
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