Use synthetic division and the Remainder Theorem to evaluate \( P(c) \). \[ \begin{array}{l} P(x)=2 x^{2}+12 x+2, \quad c=-5 \\ P(-5)=\square \end{array} \] Need Help? Read It Watch it

To evaluate \( P(c) \) using synthetic division with \( c = -5 \), we set up the synthetic division using the coefficients of \( P(x) = 2x^2 + 12x + 2 \), which are \( 2, 12, 2 \). We line up \( -5 \) to the left: \[ \begin{array}{r|rrrr} -5 & 2 & 12 & 2 \\ & & -10 & -10 \\ \hline & 2 & 2 & -8 \\ \end{array} \] The last number, \(-8\), represents \( P(-5) \). The Remainder Theorem states that if you divide a polynomial by \( (x - c) \), the remainder is \( P(c) \). Here, since we started with \( c = -5 \), \( P(-5) \) is indeed the remainder, which means \( P(-5) = -8 \). Therefore, \( P(-5) = \square \) is \(-8\).