this is what u do on your first problem....first u take out the greatest common factor that would go into all of them...
4n^2-20n+24...now what number will go into all of them...well 4 will...4 will go into 4,20,and 24...so.
it would be like this..4(n^2-5n+6)...then theirs one more step...4(n-2)(n-3)
4x^2-22x+10 would be...2(2x^2-11x+5)...then u factor again...2(2x-1)(x-5)
1/2x^2-1/2would be 1/2(x^2-1)...then u factor again...1/2(x+1)(x-1)
Factor:
4n²-20n+24
4x²-22x+10
1/2x²-1/2
Thanks in advance.
On each, take out the common factor
2(2n²-10n+12)
2(2x²-11x+ 5)
1/2 (x²-1)
Now you should be able to factor the inside.
Thanks, but that's where I get stuck. I thought like for the first one that you have to multipy two numbers together to get 12 and they have to add to -10. I can't think of 2 numbers, or am I just doing it wrong?
No worries! Factoring can be a bit tricky, but with practice, it becomes easier.
Let's take a closer look at your first problem:
2(2n² - 10n + 12)
To factor the trinomial 2n² - 10n + 12, we need to find two numbers that multiply to give the constant term (12) and add up to the coefficient of the linear term (-10).
In this case, we are looking for two numbers that multiply to give 12 and add up to -10. One way to determine these numbers is by listing all possible factor pairs of 12:
1 and 12
2 and 6
3 and 4
Now, let's see if any of these pairs add up to -10.
1 + 12 = 13
2 + 6 = 8
3 + 4 = 7
None of these pairs adds up to -10. Therefore, we cannot factor the trinomial using integer factors.
However, there is another technique we can use called factoring by grouping. Here's how it works:
1. Split the middle term, -10n, into two terms such that their coefficients multiply to give the product of the coefficient of the square term (2) and the constant term (12). In this case, that product is 24.
2. Rewrite the trinomial, grouping the terms properly:
2n² - 10n + 12 = 2n² - 4n - 6n + 12
3. Now, factor by grouping:
2n² - 4n - 6n + 12 = 2n(n - 2) - 6(n - 2)
4. Notice that we now have a common binomial term, (n - 2). We can factor it out:
2n(n - 2) - 6(n - 2) = (n - 2)(2n - 6)
So, the factored form of the trinomial 2(2n² - 10n + 12) is (n - 2)(2n - 6).
I hope this helps! Let me know if there's anything else you need assistance with.