Question
Factor the expression completely: \[ x^{3}+3 x^{2}+2 x \]
Ask by Ellis Hammond. in the United States
Mar 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression \( x^{3}+3x^{2}+2x \) factors completely to \( x(x+1)(x+2) \).
Solution
Factor the expression \( x^{3}+3x^{2}+2x \).
Factor the expression by following steps:
- step0: Factor:
\(x^{3}+3x^{2}+2x\)
- step1: Rewrite the expression:
\(x\times x^{2}+x\times 3x+x\times 2\)
- step2: Factor the expression:
\(x\left(x^{2}+3x+2\right)\)
- step3: Factor the expression:
\(x\left(x+1\right)\left(x+2\right)\)
The expression \(x^{3}+3x^{2}+2x\) can be factored completely as \(x(x+1)(x+2)\).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Mind Expander
To factor the expression \( x^{3}+3 x^{2}+2 x \) completely, we first factor out the greatest common factor, which is \( x \): \[ x(x^{2} + 3x + 2) \] Next, we need to factor the quadratic expression \( x^{2} + 3x + 2 \). We look for two numbers that multiply to \( 2 \) (the constant term) and add to \( 3 \) (the coefficient of \( x \)). The numbers are \( 1 \) and \( 2 \). Thus, we can write: \[ x^{2} + 3x + 2 = (x + 1)(x + 2) \] Now substituting this back into our expression, we get: \[ x(x + 1)(x + 2) \] So, the completely factored form of the expression \( x^{3}+3 x^{2}+2 x \) is: \[ x(x + 1)(x + 2) \]
