I am down to 5 out of 49 problems that I can't figure out. Help is very much appreciated. Thanks !
Factor by grouping:
x^3 + 8x^2 -5x -40=
I have (x^2 -5)(x + 8) ????
correct
Thanks Reiny
To factor the given expression using the method of grouping, follow these steps:
Step 1: Split the middle term
Start by splitting the middle term (-5x) into two terms such that their coefficients multiply to give the product of the coefficient of the quadratic term (8x^2) and the constant term (-40). In this case, the product is (-5)(-40) = 200. We need to look for two numbers whose product is 200 and whose sum is the coefficient of the middle term (-5x).
After examining the factors of 200, we find that -10 and 20 satisfy these conditions because -10 * 20 = 200 and -10 + 20 = 10.
Step 2: Group the terms
Group the terms in pairs and factor them separately. In this case, we can group the terms as follows:
(x^3 + 20x^2) + (-10x - 40)
Step 3: Factor out the common terms from each group
From the first group, we can factor out the greatest common factor (GCF) of x^2, which gives us:
x^2(x + 20)
From the second group, we can factor out the greatest common factor (GCF) of -10, which gives us:
-10(x + 4)
Step 4: Factor out the GCF of the entire expression
Looking at the factored groups, we can observe that both groups have a common factor (x + 20). Thus, we can factor out the (x + 20) term, which gives us:
(x^2 - 10)(x + 20)
Therefore, the fully factored form of the expression x^3 + 8x^2 - 5x - 40 is: (x^2 - 10)(x + 20)
It seems that the factorization you provided, (x^2 - 5)(x + 8), is not correct.