Please help me factor this by grouping. I am stuck.
7x^3-35x^2-6x+30
7x^3 - 35x^2 - 6x + 30
Factor 7x^2 from the first two terms and -6 from the last two terms.
Thank you.. SO would it be
(x-5)(x+5)
7x^2(x-5)-6(x-5)...
Well, let's try your answer:
(x-5)(x+5)
= x^2 - 25. So, that doesn't work.
Doing the factoring I mentioned previously gives:
7x^2(x - 5) - 6(x - 5)
Now there are two terms. The terms have a common factor of (x-5). Using our friendly distributive law we can write:
(7x^2-6)(x-5)
Thank you so so much for your help.
Your very welcome!
To factor the expression 7x^3 - 35x^2 - 6x + 30 by grouping, we can follow these steps:
Step 1: Group the terms in pairs.
Divide the expression into two pairs, each containing two terms:
(7x^3 - 35x^2) - (6x - 30)
Step 2: Factor out the greatest common factor (GCF) from each pair.
From the first pair, we can factor out 7x^2:
7x^2(x - 5)
From the second pair, we can factor out -6:
-6(x - 5)
Step 3: Check if the factors for each pair are the same.
In this case, the factors (x - 5) from both pairs are the same.
Step 4: Combine the factored pairs.
Combine the factored pairs with the common factor (x - 5):
(7x^2 - 6)(x - 5)
Therefore, the factored form of the expression 7x^3 - 35x^2 - 6x + 30 is (7x^2 - 6)(x - 5).