Factor: 3x^3-4x^2-15z+20
I used mathway found out it is (3x-4)(x^2-5)
But I am not sure how they did it...
I only got to x(3x+5)(x-3)+20
Your help is greatly appreciated!!
3x^3-4x^2-15x+20
factor by grouping.
x^2(3x-4) - 5(3x-4)
(x^2-5)(3x-4)
Sorry the equation had a typo, it should be 3x^3-4x^2-15x+20
👍 👍 I see it now.. 😆
Thank you so much oobleck :）
To factor the expression 3x^3 - 4x^2 - 15z + 20, let's break it down step by step:
Step 1: Group the terms.
3x^3 - 4x^2 - 15z + 20
Step 2: Look for common factors.
In this case, there isn't a common factor in all the terms.
Step 3: Factor by grouping.
To factor by grouping, we group the terms in pairs, looking for common factors within each pair.
We can group the terms as shown:
(3x^3 - 4x^2) - (15z - 20)
Now, let's factor out the greatest common factor from each pair separately:
From the first group (3x^3 - 4x^2), we can factor out x^2:
x^2(3x - 4)
From the second group (15z - 20), we can factor out 5:
-5(3z - 4)
So, now we have:
x^2(3x - 4) - 5(3z - 4)
Step 4: Check if there are any common factors left.
In this case, we can see that (3x - 4) is a common factor in both terms. So, we can factor it out:
x^2(3x - 4) - 5(3z - 4)
= (3x - 4)(x^2 - 5)
Therefore, the fully factored expression is (3x - 4)(x^2 - 5).
It seems that you made a small mistake in your attempted solution. Let's review it:
x(3x + 5)(x - 3) + 20
Your initial step of grouping the terms is correct, but when factoring, you mistakenly used different expressions.
Remember to factor out the greatest common factor separately for each group of terms and then check for any common factors remaining.