Factor Completely
20w^2+100w+40
20(w^2+5w+2)
Quadratic formula again..
20w^2+100w+40
20(w+ )(w+ )
_ * _ = a*c = 800
_ + _ = b =
This is where I am stuck in solving this question - please advise ty:)
To factor completely, we need to find the greatest common factor (GCF) of all the terms and then apply factoring techniques like factoring by grouping or quadratic factorization.
In this case, let's first look for the GCF.
The coefficients of the terms are 20, 100, and 40. The GCF of these coefficients is 20. We can factor out 20 from each term:
20w^2 + 100w + 40
= 20(w^2 + 5w + 2)
Now, let's focus on the expression inside the parentheses: w^2 + 5w + 2. This expression doesn't seem to be factorable using simple linear factors, so we can apply quadratic factorization.
To factor a quadratic expression of the form ax^2 + bx + c, we need to find two binomials (in the form of x + m and x + n) such that their product gives us ac (the product of the coefficients of the quadratic term and the constant term) and their sum gives us b (the coefficient of the linear term).
In this case, a = 1, b = 5, and c = 2. The product of a and c is 1 * 2 = 2, and the sum of m and n is 5.
We are looking for two numbers whose product is 2 and whose sum is 5. The numbers that satisfy this condition are 2 and 1.
Therefore, we can rewrite the expression as:
w^2 + 5w + 2 = (w + 2)(w + 1)
Putting it all together, the factored form of the expression 20w^2 + 100w + 40 is:
20(w + 2)(w + 1)