Need help please explain how to get the answers for these two factoring problems and for the second problem with the "ac method".
2a^2+1+3a
15x^2+31x+2
take a read here:
https://people.richland.edu/james/misc/acmeth.html
See previous post: Thu, 8-7-14, 11:29PM.
Sure! I'd be happy to help explain how to solve these factoring problems.
Problem 1: 2a^2 + 1 + 3a
To factor this expression, we look for common factors and grouping.
Step 1: Look for common factors
In this case, there are no common factors among the terms.
Step 2: Grouping
Since we can't find any common factors, we will use the grouping method. We will group the first two terms together and the last two terms together.
2a^2 + 1 + 3a
(2a^2 + 3a) + 1
Step 3: Look for common factors within each group
In the first group, we can factor out an 'a':
a(2a + 3) + 1
Step 4: Check for any further common factors
In this case, there are no further common factors.
So, the factored form of the expression 2a^2 + 1 + 3a is: a(2a + 3) + 1
Problem 2: 15x^2 + 31x + 2
For solving this problem using the "ac method," we look for two numbers whose product is equal to the product of the coefficients of the first and last term, and whose sum is equal to the coefficient of the middle term.
In this case, the coefficient of x^2 is 15, the coefficient of x is 31, and the constant term is 2.
Step 1: Find the product and sum
We need to find two numbers whose product is equal to (15 * 2) = 30 and whose sum is equal to 31.
The numbers that satisfy these conditions are 30 and 1. (These numbers are obtained by listing and testing the factor pairs of 30.)
Step 2: Split the middle term using the numbers found
We rewrite the middle term, 31x, as the sum of 30x and 1x:
15x^2 + 30x + 1x + 2
Step 3: Grouping
Now, we group the terms:
(15x^2 + 30x) + (1x + 2)
Step 4: Factor out the greatest common factor from each group
In the first group, we can factor out 15x:
15x(x + 2) + (1x + 2)
Step 5: Check for any further common factors
In this case, there are no further common factors.
So, the factored form of the expression 15x^2 + 31x + 2 using the AC method is: 15x(x + 2) + (1x + 2)