Which of these is a factor of [tex]$x^3-3 x^2$[/tex]?
A) [tex]$x+2$[/tex]
B) [tex]$x+3$[/tex]
C) [tex]$x-3$[/tex]
D) [tex]$x-2$[/tex]

The problem requires us to identify a factor of the polynomial x 3 − 3 x 2 . We factor the polynomial as x 2 ( x − 3 ) . Comparing this with the given options, we find that x − 3 is a factor. Therefore, the answer is x − 3 ​ .
Explanation

Understanding the Problem We are given the polynomial x 3 − 3 x 2 and asked to identify which of the options is a factor of this polynomial. A factor is an expression that divides the polynomial evenly, leaving no remainder.

Factoring the Polynomial To find the factors, we first factor the given polynomial. We can factor out the greatest common factor, which is x 2 . This gives us: x 3 − 3 x 2 = x 2 ( x − 3 ) So, the factors of the polynomial are x 2 and ( x − 3 ) .

Identifying the Factor Now we compare the factored form with the given options: A) x + 2 B) x + 3 C) x − 3 D) x − 2 We see that ( x − 3 ) is one of the factors of the polynomial.

Final Answer Therefore, the correct answer is C) x − 3 .


Examples
Factoring polynomials is a fundamental skill in algebra and is used in many real-world applications. For example, engineers use factoring to simplify complex equations when designing structures or circuits. Imagine you are designing a rectangular garden with an area represented by the expression x 3 − 3 x 2 . By factoring this expression to x 2 ( x − 3 ) , you can determine possible dimensions for the garden. One side could have a length of x 2 and the other side a length of x − 3 . This allows for easier planning and construction of the garden.

Answered by GinnyAnswer | 2025-07-07