Question

In the following exercises, factor each trinomial of the form $x^2+bx+c$.

$y^2-5y+6$

Short answer

The factorization is $(y-2)(y-3)$.

Step-by-step solution

Step 1. Writing the expression

Write the factors as two binomials with first terms $y$.

$(y)(y)$

Step 2. Finding the factors

We need to find two numbers whose product is $6$and sum is $-5$.

Factors of 6	Sum of factors
$-1,-6$	$-7$
$-2,-3$	$-5$

Thus, $-2$and $-3$are the correct factors.

Hence, the factorization is$(y-2)(y-3)$.

Step 3. Check

Multiply the factorization to get the trinomial again.

$$\begin{gathered} (y-2)(y-3)=y^2-3y-2y+6 \\ (y-2)(y-3)=y^2-5y+6 \end{gathered}$$

Thus, the obtained factorization is correct.