Answer:
1. The zeros are at x = 0 and x = –10
2. The zeros are at x = 3 and x = 4
Explanation:
1. f(x) = x (x + 10)
Multiplying any number by 0 = 0,
so f(x) = 0 when...
• x = 0
or
• x + 10 = 0 (if you subtract 10 from both sides, you get x = –10)
2. f(x) = x (x - 3) – 4 (x - 3)
Use distributive property to expand
x² – 3x – 4x + 12
Combine like terms
x² – 7x + 12
Factor
(x – 3) (x – 4)
(You could have also just noticed in the original function that both x and –4 were multiplied by (x – 3) and factored then.)
So f(x) = 0 when...
• x – 3 = 0 (add 3 to both sides to get x = 3)
or
• x – 4 = 0 (add 4 to both sides to get x = 4)
I hope that helped!