how do u factor 5w^2-35w+60=0
if u could...can y plz explain it..i keep getting 3 ansers instead of 2
Start by factoring out a 5 from each term. What do you come up with?
i got 5(w^2-7w+12)=0...is that right?..and then do i factor the middle?...but when i did i get 3 answers
Yes, that's good.
You're going to want something in the form (__ + __)(__ + __)
One or both of the signs could be negative, though.
Look at the 12. What are its two closest factors? When added, do they equal 7?
You can check yourself by using the FOIL method after you come up with your factorization. Now, what do you get?
I should mention that you are ignoring the 5 now and working solely with w^2-7w+12.
i got 5(w-3)(w-4)...that i totally understand...now i put 5=0 w-3=0 and w-4=0...hmm...i see wat i did now..one last question wat do i do with the 5=0?
You just ignore the 5, as 5 cannot equal 0. Your answers are just w = 3 and w = 4.
thank u very very much...that helped ALOT
Glad to help. :)
To factor the quadratic equation 5w^2 - 35w + 60 = 0, follow these steps:
Step 1: Check if there is a common factor among all the terms.
In this case, there isn't a common factor among all three terms.
Step 2: Ensure that the quadratic equation is in the standard form, ax^2 + bx + c = 0, with a coefficient of 1 for the squared term.
The given equation, 5w^2 - 35w + 60 = 0, is in the standard form.
Step 3: Factor the quadratic trinomial.
To factorize, we need to find two binomials that multiply to give the trinomial.
We start by multiplying the coefficient of the squared term and the constant term: (5)(60) = 300.
We need to find two numbers that add up to the coefficient of the linear term (-35) and multiply to give the constant term (300).
The factors of 300 are:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
Let's find two numbers that add up to -35: -5 and -60.
These two numbers multiply to give 300 (-5 * -60 = 300), and they add up to -35 (-5 + -60 = -65).
Step 4: Write the factors in the form of binomials.
Replace the middle term (-35w) with the factors we found (-5w and -60w) to split the quadratic equation.
5w^2 - 5w - 60w + 60 = 0
Step 5: Group the terms and factor by grouping.
Now, we will group the terms in pairs and take out the common factors from each group.
(5w^2 - 5w) + (-60w + 60) = 0
Take out the common factors:
5w(w - 1) - 60(w - 1) = 0
Now, we can observe a common binomial factor, (w - 1), from both terms:
(w - 1)(5w - 60) = 0
Step 6: Solve for w from each binomial factor.
To get the possible values of w, we set each binomial factor equal to zero and solve for w:
w - 1 = 0 --> w = 1
5w - 60 = 0 --> 5w = 60 --> w = 12
Therefore, the solutions for the given quadratic equation are w = 1 and w = 12.
So, the factored form of the equation 5w^2 - 35w + 60 = 0 is (w - 1)(5w - 60) = 0, and the solutions are w = 1 and w = 12.