how do you factor 18c^4-9c^2+7c ?
To Factor:
1) Find the Greatest Common Factor
2) Solve the trinomial (if their is one)
3) Find the difference of perfect square (if their is one)
So: the factors of 18,9, and 7
18c: 1c,2c,3c,6c,9c,18c
9c: 1c,3c,9c
7c: 1c,7c
So the GCF is C
yes
To factor the expression 18c^4 - 9c^2 + 7c, we can follow these steps:
Step 1: Look for the greatest common factor (GCF) of all the terms, if any. In this case, there is no common factor among the terms.
Step 2: Check if the expression has a common binomial factor. A common binomial factor means that both the coefficient and the variable are the same. In this case, there is no common binomial factor.
Step 3: Determine if the expression can be factored by grouping. Grouping involves grouping the terms together in a way that allows us to factor out a common factor. However, for this expression, there is no simple way to group the terms and factor them out.
Step 4: Since the expression cannot be factored easily, we can use a method called factoring by substitution. Let's substitute a variable to make it easier to factor. Let u = c^2.
Substituting u = c^2 into the expression, we get: 18u^2 - 9u + 7c.
Step 5: Now, let's factor the expression 18u^2 - 9u + 7c. This expression is a quadratic trinomial. We can either use factoring techniques or the quadratic formula to factor it. However, since we substituted u = c^2 earlier, we need to back-substitute to express the final answer in terms of c.
Therefore, the factored form of 18c^4 - 9c^2 + 7c is: (18u - 7)(u + c).
Now, we substitute back c^2 in place of u:
(18c^2 - 7)(c^2 + c) is the factored form of 18c^4 - 9c^2 + 7c.