factoring completely, state that the polynomials is prime.
x^-16
(x+8)(x-8) not prime.
x^-8x+12
x(8x+12)
(4x+6) Check these problem me please
It seem when I turn in problem noone answer them could someone tell me why.
x^2 - 16 = (x+4)(x-4) , not what you have
x^2 - 8 + 12
= (x-6)(x-2)
Your answer makes no sense. Whenever you factor, you can check by expanding your answer, and of course you should get back the original question.
Your answers don't come even close.
Of course any polynomial which can be factored cannot be prime, just like numbers.
Ashley, I went back and checked some of your previous posts.
Some were answered, and some had a lack of brackets that made the question very unclear.
The tutors that answer questions are all volunteers and are not paid for this. Most of us are either retired or just plain enjoy helping students. You also have to consider the time at which you post question. In my case I am typing this at 12:25 in the morning.
Have patience, if your question is precise and clear, it will usually get answered.
To factor the polynomial completely, we can follow these steps:
Step 1: Look for a common factor, if any.
In the given polynomial x^-8x+12, there is no common factor other than 1.
Step 2: Check if the polynomial can be factored using any factoring formulas or techniques.
In this case, we can use the quadratic factoring technique.
Step 3: Split the middle term.
The middle term in the polynomial is -8x. We need to find two numbers that multiply to give 12 and add up to -8. The numbers that satisfy this condition are -2 and -6.
Step 4: Rewrite the polynomial using the split terms.
The polynomial can be rewritten as:
x^2 - 2x - 6x + 12
Step 5: Group the terms and factor by grouping.
Taking pairs of terms, we can factor by grouping:
(x^2 - 2x) + (-6x + 12)
x(x - 2) - 6(x - 2)
Step 6: Factor out the common binomial.
From the grouped terms, we can factor out the common binomial (x - 2):
(x - 2)(x - 6)
Thus, the factored form of the polynomial x^-8x+12 is (x - 2)(x - 6).
To check if the resulting factored expression is correct, you can expand it by multiplying the factors. In this case:
(x - 2)(x - 6) = x^2 - 2x - 6x + 12 = x^2 - 8x + 12
This confirms that (x - 2)(x - 6) is the correct factored form of the given polynomial.
Please note that the term "prime" is typically used to describe numbers, not polynomials. However, if you meant to ask whether the factored polynomial (x - 2)(x - 6) is irreducible or cannot be factored further, then the answer is yes.