SOLUTION: I need to factor the following and provide pairs of factors and sums of factors
I don't quite get the text book
X with exponential of 2 +8x+15
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-> SOLUTION: I need to factor the following and provide pairs of factors and sums of factors
I don't quite get the text book
X with exponential of 2 +8x+15
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Question 76401This question is from textbook Developmental Mathematics
: I need to factor the following and provide pairs of factors and sums of factors
I don't quite get the text book
X with exponential of 2 +8x+15 This question is from textbook Developmental Mathematics
You can put this solution on YOUR website! Factor:
.
.
Since the multiplier of the term is 1, you know that the factors must be of the
form:
.
(x __ ___)*(x __ ___)
.
Notice that if you multiply these two leading factors, the result is the
that we need.
.
The two underscored blanks in each set of parentheses represent the sign (positive or negative)
and the number value. Notice that the two numbers must be factors of 15 so that when they
are multiplied they produce +15. Therefore they need to be either 1 and 15 or 3 and 5
so that they produce 15. For this problem they must both be positive or both be negative
so that their product is positive 15. The two numbers must also produce +8 when they are
added algebraically because +8 is the multiplier of the middle term. 15 and 1 cannot
produce +8 but 3 and 5 can work. So let's put them into our factors to get:
.
(x __ 3)(x __ 5)
.
Notice again that multiplying the first two terms in each set of parentheses you get x-squared
and multiplying the last terms in each set of parentheses gives you 15.
.
Are the signs both plus or both minus? The 3 and the 5 must add to be + 8 not -8. Therefore,
the signs in our factors must both be +. So our factors are:
.
(x + 3)(x + 5)
.
If you can multiply these two factors together you will find that they result in:
.
.
which checks and verifies that our factors are correct.
.
Hope that this supplements what your book says in such a way that it enables you to understand
the basic process. The process basically involves factoring the first term and then
factoring the last term. If the factors of the first term are 1x and 1x then the factors
of the last terms must be capable of producing the value of the middle term when they are
added. You need to watch the sign of the last term and the middle term so that you can
determine if the factors need to be both +, both - , or one + and one -. After working a
few problems such as this one, you will get the hang of it.
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