Factoring x² + 2x Step-by-Step
Given the expression: x² + 2x
Step 1: Understand the Expression
The given expression has two terms: x² and 2x.
Step 2: Break Down Each Term
We can rewrite x² as x * x and 2x as 2 * x.
Step 3: Identify the Common Factor
Look at both terms (x * x and 2 * x). The factor ‘x’ appears in both terms. It’s the common factor.
Step 4: Factor Out the Common Factor
Take out the ‘x’ from both terms.
x(x + 2)
Step 5: Final Factored Form
The expression is now factored as x(x + 2)
Factoring x² – 3x Step-by-Step
Given the expression: x² – 3x
Step 1: Understand the Expression
The given expression has two terms: x² and -3x.
Step 2: Break Down Each Term
We can rewrite x² as x * x and -3x as -3 * x.
Step 3: Identify the Common Factor
Look at both terms (x * x and -3 * x). The factor ‘x’ appears in both terms. It’s the common factor.
Step 4: Factor Out the Common Factor
Take out the ‘x’ from both terms.
x(x – 3)
Step 5: Final Factored Form
The expression is now factored as x(x – 3)
Factoring -x² – 5x Step-by-Step
Given the expression: -x² – 5x
Step 1: Understand the Expression
The given expression has two terms: -x² and -5x.
Step 2: Break Down Each Term
We can rewrite -x² as -1 * x * x and -5x as -5 * x.
Step 3: Identify the Common Factor
Look at both terms (-1 * x * x and -5 * x). The factors ‘-1’ and ‘x’ appear in both terms, making them the common factors.
Step 4: Factor Out the Common Factors
Take out the ‘-1’ and ‘x’ from both terms.
-1 * x * (x + 5)
Step 5: Final Factored Form
The expression is now factored as -1 * x * (x + 5) or -x(x + 5)
Factoring \( \frac{x^2}{4} – \frac{3x}{2} \) Step-by-Step
Given the expression: \( \frac{x^2}{4} – \frac{3x}{2} \)
Step 1: Understand the Expression
The given expression has two terms: \( \frac{x^2}{4} \) and \( -\frac{3x}{2} \).
Step 2: Break Down Each Term
We can rewrite \( \frac{x^2}{4} \) as \( \frac{1}{4} \times x \times x \) and \( -\frac{3x}{2} \) as \( -\frac{3}{2} \times x \).
Step 3: Identify the Common Factor
Look at both terms \( \left( \frac{1}{4} \times x \times x \right) \) and \( \left( -\frac{3}{2} \times x \right) \). The common factor is \( x \).
Step 4: Factor Out the Common Factor
Take out the \( x \) from both terms.
\[ x \left( \frac{x}{4} – \frac{3}{2} \right) \]
Step 5: Final Factored Form
The expression is now factored as \( x \left( \frac{x}{4} – \frac{3}{2} \right) \)