Answer:
The factored form (y - 3)(y + 6) is indeed correct.
Step-by-step explanation:
1. Identify the coefficients:
The quadratic expression is ( y² + 3y - 18 ).
The coefficient of ( y² ) (a) is 1.
The coefficient of ( y ) (b) is 3.
The constant term (c) is -18.
2. Find two numbers that multiply to
[tex]( a \cdot c ) (1 \cdot -18 = -18)[/tex]
and add up to ( b ) (3):
• We need to find two numbers that multiply to -18 and add up to 3.
• These numbers are 6 and -3 because ( 6 x (-3) = -18 ) and ( 6 + (-3) = 3 ).
3. Rewrite the middle term using these two numbers:
[tex]y² + 6y - 3y - 18[/tex]
4.Factor by grouping:
[tex](y² + 6y) + (-3y - 18)[/tex]
y(y + 6) - 3(y + 6)
5. Factor out the common binomial factor:
[tex](y - 3)(y + 6)[/tex]
