Question

Factor the trinomial completely. If the trinomial contains a greatest common factor (other than 1), factor out the GCF first.

2x³-14x² + 20x
CCCON

Answer 1

2x(x - 2)(x - 5)

Explanation:

To factor the trinomial 2x³ - 14x² + 20x completely, let's first look for the greatest common factor (GCF) among the terms.

The GCF of the terms 2x³, -14x², and 20x is 2x. By factoring out the GCF, we get:

=> 2x(x² - 7x + 10)

Now, let's factor the quadratic trinomial inside the parentheses: x² - 7x + 10. This can be factored as follows:

=> x² - 7x + 10 = (x - 5)(x - 2)

Therefore, the completely factored form of the trinomial 2x³ - 14x² + 20x is:

=> 2x(x - 5)(x - 2)