A polynomial p(y) is given as ay^12+by^5-c where a,b and c are natural numbers. Is 0 a zero of p(y) Choose 1 answer:

if 0 is a zero of the polynomial \( p(y) = ay^{12} + by^{5} - c \), we need to evaluate \( p(0) \).<br /><br />Substitute \( y = 0 \) into the polynomial:<br />\[ p(0) = a(0)^{12} + b(0)^{5} - c \]<br /><br />Since any number raised to the power of 0 is 1, we have:<br />\[ p(0) = a \cdot 1 + b \cdot 1 - c \]<br />\[ p(0) = a + b - c \]<br /><br />For 0 to be a zero of the polynomial, \( p(0) \) must be equal to 0:<br />\[ a + b - c = 0 \]<br /><br />Therefore, 0 is a zero of \( p(y) \) if and only if \( a + b = c \).