4. Factoring to Solve Quadratic Equations
Sign In
To factor a trinomial with a leading coefficient of 1, think of the process as multiplying two binomials in reverse.
(y-5)^2
Factor Constants | Product of Constants |
---|---|
1 and 25 | 25 |
-1 and -25 | 25 |
5 and 5 | 25 |
-5 and -5 | 25 |
Next, let's consider the coefficient of the linear term. y^2-10y+25 For this term, we need the sum of the factors that produced the constant term to equal the coefficient of the linear term, -10.
Factors | Sum of Factors |
---|---|
1 and 25 | 26 |
-1 and -25 | -26 |
5 and 5 | 10 |
-5 and -5 | -10 |
We found the factors whose product is 25 and whose sum is -10. y^2-10y+25 ⇔ (y-5)(y-5) Both factors are the same, so we can write the expression as (y-5)^2.