1.How do you factor (-5t^2+50t+5) ? I keep getting (-5)(t-1)(t+1), but when I check it by foiling and multiplying, it doesn't equal the original trinomial.
2. Can I multiply (-3x-2x+8) by (-1) to get rid of the negative coefficient? If I don't, it will be differently factored, but will still be "correct". Which one is the right answer?
-5t^2+50t+5
= -5(t^2 - 10t - 1)
that's it
you can't just "get rid of " the negative, you can factor it out, but you must keep it
did you mean that to say:
-3x^2 - 2x + 8 ??
I will assume you did.
= -3(3x^2 + 2y - 8)
= -3(x+4)(x-2)
or
= 3(x+4)(2-x)
can you see what I just did?
For #1, I see what I did. I got the right answer, but then i tried to factor it more, even though it was completely factored.
For #2 you are right, i did mean -3x^2. I am still a little confused, why did you do the whole distributing by three? What we've learned with a trinomial (that has no common factor) is that you use a guess and check method. I can see where I'm wrong about multiplying the whole trinomial by (-1), but I get lost from there. Can you explain?
Sorry let me clarify. Why did you pull 3 out of the trinomial?
Sorry about that 2nd one, I messed that one up badly.
I guess I was somehow focused on that -3
ok, here goes ....
-3x^2 - 2x + 8
= -1(3x^2 + 2x - 8)
= -1((3x - 4)(x + 2)
or
(4 - 3x)(x+2)
Okay that looks right :) Could tell me your steps though? I can see that its right, I just don't really know how you got there.
1. To factor the trinomial (-5t^2 + 50t + 5), we can follow a systematic approach:
First, check if there is a common factor among the terms. In this case, the common factor is 5:
(-5t^2 + 50t + 5) = 5(-t^2 + 10t + 1)
Next, we look for a pair of numbers that adds up to the coefficient of the middle term (10) and multiplies to give the product of the first and last terms (-1). In this case, it is +1 and +1:
5(-t^2 + 10t + 1) = 5(-t^2 + t + 10t + 1)
Now, group the terms together:
5[-(t^2 - t) + (10t + 1)] = 5[-t(t - 1) + 1(10t + 1)]
Finally, factor out the common factor from each group:
5(t - 1)(-t + 10t + 1) = 5(t - 1)(9t + 1)
Therefore, the correct factored form of (-5t^2 + 50t + 5) is 5(t - 1)(9t + 1), not (-5)(t - 1)(t + 1).
It's essential to double-check your work by expanding the factored form to ensure it equals the original trinomial.
2. Yes, you can multiply (-3x - 2x + 8) by (-1) to get rid of the negative coefficient. Multiplying every term in the expression by (-1) changes the signs, resulting in:
(-1)(-3x - 2x + 8) = (3x + 2x - 8)
So, the result of multiplying (-3x - 2x + 8) by (-1) is equivalent to (3x + 2x - 8).
Both expressions have the same terms but arranged differently. Either form can be considered "correct," as long as the terms and factors are accurate. The choice of which form to use may depend on the context or personal preference.