Q 69E - Intermediate Algebra

Question

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

$y^2-18y+45$

Step-by-Step Solution

Answer

The factorization is $(y-3)(y-15)$.

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 $45$ and sum is$-18$.

Factors of 45	Sum of factors
$-1, -45$	$-46$
$-3, -15$	$-18$
$-5, -9$	$-14$

Thus, $-3$ and $-15$ are the correct factors.

Hence, the factorization is $(y-3)(y-15)$.

Step 3. Check

Multiply the factorization to get the trinomial again.

$$\begin{gathered} (y-3)(y-15)=y^2-15y-3y+45 \\ (y-3)(y-15)=y^2-18y+45 \end{gathered}$$

Thus, the obtained factorization is correct.