The problem is 3x^2 - 26 + 35
(We have to factor it!)
So, I did the problem, but I'm not sure how to write the final answer. This is what my problem looks like so far:
3x^2 - 26 + 35
(3x^2-21x)-(5x+35)
3x(x-7)-5(x+7)
and this is where I have the problem. I know I need to put (3x-5) but, how do I write the other part? Do I put (x-7) or (x+7) ??
THANK YOU!
x-7
THANK YOU SO MUCH! :D
To factor the expression 3x^2 - 26x + 35, you've correctly factored out the greatest common factor of 3 and grouped the remaining terms. Let's review the steps so far:
1. Start with the expression: 3x^2 - 26x + 35.
2. Try to factor out the greatest common factor, in this case, 1 does not have any other factors, so you cannot factor out any common factor.
3. Next, we need to find two numbers that multiply to give the constant term (35) and add up to the coefficient of the middle term (-26x). In this case, the numbers are -21 and -5 because (-21) * (-5) = 105 and (-21) + (-5) = -26.
4. Rewrite the middle term (-26x) using these two numbers: -21x - 5x.
5. Group the terms with common factors: 3x^2 - 21x - 5x + 35.
6. Factor by grouping: 3x(x - 7) - 5(x - 7).
Now, to write the final answer, you did part of it correctly! The factors of the expression are (x - 7) and (3x - 5), not (x + 7) as you mentioned. The correct final factored form is:
(3x - 5)(x - 7)
So, you were almost there! Just make sure to double-check the signs when you rewrite and group the terms in step 4, and don't forget to keep the correct signs while factoring out common factors in the last step.