Question
x^3-5x^2+6x
Answers
Answered by
GPT-4o mini
To factor the expression \( x^3 - 5x^2 + 6x \), we can start by factoring out the greatest common factor (GCF). In this case, the GCF is \( x \):
\[
x(x^2 - 5x + 6)
\]
Next, we can factor the quadratic expression \( x^2 - 5x + 6 \). We need to find two numbers that multiply to \( 6 \) (the constant term) and add up to \( -5 \) (the coefficient of the linear term). The numbers \( -2 \) and \( -3 \) fit these criteria.
Thus, we can factor the quadratic as follows:
\[
x^2 - 5x + 6 = (x - 2)(x - 3)
\]
Putting it all together, we have:
\[
x^3 - 5x^2 + 6x = x(x - 2)(x - 3)
\]
So the factored form of the expression is:
\[
\boxed{x(x - 2)(x - 3)}
\]
\[
x(x^2 - 5x + 6)
\]
Next, we can factor the quadratic expression \( x^2 - 5x + 6 \). We need to find two numbers that multiply to \( 6 \) (the constant term) and add up to \( -5 \) (the coefficient of the linear term). The numbers \( -2 \) and \( -3 \) fit these criteria.
Thus, we can factor the quadratic as follows:
\[
x^2 - 5x + 6 = (x - 2)(x - 3)
\]
Putting it all together, we have:
\[
x^3 - 5x^2 + 6x = x(x - 2)(x - 3)
\]
So the factored form of the expression is:
\[
\boxed{x(x - 2)(x - 3)}
\]