Question

help please
factor the polynomial completely
4y^2+12y+5

Answer 1

Hint:
4y^2 + 10y + 2y + 5

Answer 2

???

Answer 3

It's a method called factor by grouping

Answer 4

Let me show you the full steps and see if you can understand it:

The essential idea behind factor by grouping is this:
Given any polynomial of the form ax^2 + bx + c
1. Find two numbers that add to get b, but multiply to get ac
2. Split the middle term using the two numbers you find
3. Factor the first two terms, then factor the last two terms
4. Factor out the remaining binomial.
5. The final form will be the product of two binomials

In your case, you have the following:
Given polynomial: 4y^2+12y+5

1. 10 and 2 multiplies to get 20, but adds to get 12
2. 4y^2+12y + 5 is split to 4y^2 + 10y + 2y + 5
3. Factoring the first two terms and the last two terms we get 2y(2y+5)+1(2y+5)
4. Factoring out the remaining binomial (2y+5) we get:
5. (2y+5)(2y+1)

Any questions?