4y2 + 25y + 6
can you explain how to do step by step thanks
Factor completely
You do it trial and error:
start with the y^2 factor
4,1
1,4
2,2
Then the six factors
6,1
1,6
3,2
2,3
put them together, need to make 25
Hmmm 4*6 +1*1 makes 25.
I hope that helps.
I had asked you earlier, what methods you had learned, but you changed your name again.
You will have to let me know which method I should explain, I use about 3 different methods.
To factor the quadratic expression 4y^2 + 25y + 6 completely, you can follow these steps:
Step 1: Check if the expression can be factored by grouping or using any factoring formula. In this case, the expression cannot be factored by grouping or any specific factoring formula.
Step 2: Look for two numbers that multiply to give the product of the coefficient of the quadratic term (4 in this case) and the constant term (6 in this case), and also add up to give the coefficient of the linear term (25 in this case). The numbers that meet these criteria are 1 and 6.
Step 3: Rewrite the middle term (25y) using the found numbers. We can write it as: 1y + 24y. So, the expression becomes: 4y^2 + 1y + 24y + 6.
Step 4: Group the terms in pairs. We can group the first two terms (4y^2 and 1y) together and the last two terms (24y and 6) together. The expression now becomes: (4y^2 + 1y) + (24y + 6).
Step 5: Factor out the greatest common factor (GCF) from each group. From the first group, we can factor out y, and from the second group, we can factor out 6. So, the expression becomes: y(4y + 1) + 6(4y + 1).
Step 6: Notice that we now have a common binomial factor, (4y + 1), in both terms. We can factor out this binomial factor. The expression becomes: (4y + 1)(y + 6).
Therefore, the quadratic expression 4y^2 + 25y + 6 can be factored completely as (4y + 1)(y + 6).