Answer :
The expression is equal to -15.
1. Given expression: [tex]\( \frac{c^2 - 46c \cdot 15c^3}{c^2 \cdot 4c} \div \frac{12c^3 \cdot 30c^2}{1} \)[/tex].
2. Simplifying the expression involves canceling out common factors:
[tex]\[ \frac{(c \cdot (c - 46 \cdot 15c^2))}{(c \cdot 4) \div (12 \cdot 30c)} \][/tex]
3. Further simplifying:
[tex]\[ \frac{(c \cdot (c - 690c^2))}{(4) \div (360c)} \][/tex]
4. Simplifying the numerator and denominator:
[tex]\[ \frac{c^2 - 690c^3}{90c} \][/tex]
5. Factoring out common factor c from the numerator:
[tex]\[ \frac{c \cdot (c - 690c^2)}{90c} \][/tex]
6. Canceling out common factors:
[tex]\[ \frac{c - 690c^2}{90} \][/tex]
7. Factoring out common factor c from the numerator:
[tex]\[ \frac{c \cdot (1 - 690c)}{90} \][/tex]
8. Simplifying further:
[tex]\[ \frac{-690c^2 + c}{90} = \frac{c(1 - 690c)}{90} \][/tex]
9. Simplifying:
[tex]\[ \frac{-690c^2 + c}{90} = -\frac{690c^2 - c}{90} = -\frac{c(690c^2 - 1)}{90} \][/tex]
10. Further simplifying, we get:
[tex]\[ -\frac{c(690c^2 - 1)}{90} = -\frac{c(26c + 1)(26c - 1)}{90} \][/tex]
11. Canceling out common factors:
[tex]\[ -\frac{(26c + 1)(26c - 1)}{90} \][/tex]
12. This is equivalent to -15.
Therefore, the correct answer is (c) -15.
