To factor the given polynomial [tex]\( y^2 - 6y - 3y + 18 \)[/tex], we can follow these steps:
1. Combine like terms in the polynomial:
[tex]\[
y^2 - 6y - 3y + 18 = y^2 - 9y + 18
\][/tex]
2. Identify the polynomial: We now have a quadratic polynomial [tex]\( y^2 - 9y + 18 \)[/tex].
3. Look for two binomials whose product gives the polynomial. To do this, we need to find two numbers that multiply to the constant term (18) and add up to the coefficient of the linear term (-9).
4. The two numbers that multiply to 18 and add to -9 are -6 and -3.
5. Write the polynomial as a product of binomials using these numbers:
[tex]\[
y^2 - 9y + 18 = (y - 6)(y - 3)
\][/tex]
So, the factored form of the polynomial [tex]\( y^2 - 6y - 3y + 18 \)[/tex] is:
[tex]\[
(y - 6)(y - 3)
\][/tex]
