i need help on factoring. the equation is 4x^3 - 6x^2 + 10x - 15. how do you do this problem?
2x^2(2x-3)+5(2x-3)
(2x-3)(2x^2+5)
In general, your teacher will not give you something hard without warning you first.
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To factor the given equation, 4x^3 - 6x^2 + 10x - 15, we can use a method called "factoring by grouping." The idea is to group the terms in such a way that we can factor out a common factor from each group.
Here's the step-by-step explanation on how to solve this problem using factoring by grouping:
Step 1: Group the terms in pairs.
(4x^3 - 6x^2) + (10x - 15)
Step 2: Factor out the greatest common factor from each pair.
2x^2(2x - 3) + 5(2x - 3)
Step 3: Notice that both pairs share a common term, (2x - 3).
Step 4: Factor out this common term from both groups.
(2x - 3)(2x^2 + 5)
Now, the equation 4x^3 - 6x^2 + 10x - 15 is factored as (2x - 3)(2x^2 + 5).
Using this method, we were able to identify a common factor in both groups and factor it out accordingly.