Given the function P(x)=x^3+4x^2+kx+15 for what value of k is (x+3) a factor of P(x) -26 -8 8 26

To determine the value of for which \((x+3)\) is a factor of \( P(x) = x^3 + 4x^2 + kx + 15 \), we can use the Factor Theorem. According to the Factor Theorem, \((x+3)\) is a factor of \( P(x) \) if and only if \( P(-3) = 0 \).Let's substitute into the polynomial \( P(x) \) and set it equal to zero: Now, calculate each term: So, the equation becomes: Combine the constants: Solve for : Therefore, the value of for which \((x+3)\) is a factor of \( P(x) \) is .