ello
i need help factoring
I haven't had factorin sense Algebra one and now am in Algebra two and our school is screwed up were they shove in a year of Euclidean Geometry and Basic Trig inbetween first two years of Algebra...
so i need to factor
X^2-12X+35
I can sit there for a long time and probably figure it out after a while. I forgot the thought process that's suppose to go thorugh my head to factor this instead of just thinking and checking.
So can someone please tell me the answer and what the throught process used to get there instead of just thinking and checking
thanks
This is a quadratic, so we'll try to factor it into (x+a)(x+b).
The constant term is positive, so we know that a and b have the same sign. The x term is negative, so we know a and b are both negative. We need to find two negative numbers, a and b, such that a*b = 35 and a+b = -12. You should be able to do that yourself; there aren't that many possibilities to try.
thanks
(X-7)(X-5)
subtract. Simplify if possible
z-7/z - 9z-11/11z =?
Sure, I can help you with factoring the expression X^2 - 12X + 35. Factoring involves finding the expressions or numbers that, when multiplied together, give you the original expression.
To factor the given quadratic expression, we can use the "ac method" or "splitting the middle term" method. The steps are as follows:
Step 1: Look at the coefficient of X^2, which is 1 in this case. We want to find two numbers that multiply to give us 35 (the constant term), and when added or subtracted, give us -12 (the coefficient of X). In this case, the numbers are -5 and -7.
Step 2: Rewrite the expression by splitting the middle term using the two numbers we found. Replace -12X with -5X - 7X. The expression becomes:
X^2 - 5X - 7X + 35.
Step 3: Now, group the expression into pairs:
(X^2 - 5X) + (-7X + 35).
Step 4: Factor out the greatest common factor from each pair:
X(X - 5) - 7(X - 5).
Step 5: Notice that we have a common binomial factor, (X - 5), which can be factored out:
(X - 5)(X - 7).
So, the factored form of the expression X^2 - 12X + 35 is (X - 5)(X - 7).
Now, if you were to think and check, you could try different pairs of numbers that multiply to 35 and see if any of them give you the middle term of -12. However, using the ac method is a more systematic and efficient way to factor quadratic expressions.
I hope that helps! Let me know if you have any further questions.