Question

Please someone help me, I will give you brainliest Factor the expression: y^2 + y + 1/4

Answer 1

Answer:

y² + y + $\frac{1}{4}$ = (y + $\frac{1}{2}$)²

Step-by-step explanation:

In most cases, we can factor a polynomial, or quadratic, by looking at the factors of the last term.  In this case, the last term is $\frac{1}{4}$.  When we factor a polynomial, we are looking for two expressions that when multiplied together using FOIL (forward-outside-inside-last) will give us the polynomial.  For example: (a + b)(a + b) or (a+ b)².

In order to get y² + y + $\frac{1}{4}$, we are looking for a 'c' value that will add up to '1' which is our 'b' value (ay² + by + c).

Since $\frac{1}{2}*\frac{1}{2}=\frac{1}{4}and\frac{1}{2}+\frac{1}{2}=1$

Then, we can use $\frac{1}{2}$ as our factor for both expressions.  Putting this together we get:  (y + $\frac{1}{2}$)(y + $\frac{1}{2}$) or (y + $\frac{1}{2}$)²