For the given polynomial P(x) and the given c , use the remainder theorem to find P(c) P(x)=5x^3-4x^2-3x+3;-3 P(c)= (Simplify your answer.)

To find \( P(c) \) using the Remainder Theorem, we need to substitute \( c = -3 \) into the polynomial \( P(x) \).<br /><br />Given:<br />\[ P(x) = 5x^3 - 4x^2 - 3x + 3 \]<br /><br />Substitute \( c = -3 \):<br />\[ P(-3) = 5(-3)^3 - 4(-3)^2 - 3(-3) + 3 \]<br /><br />Now, calculate each term:<br />\[ (-3)^3 = -27 \]<br />\[ 5(-27) = -135 \]<br /><br />\[ (-3)^2 = 9 \]<br />\[ -4(9) = -36 \]<br /><br />\[ -3(-3) = 9 \]<br /><br />So, we have:<br />\[ P(-3) = -135 - 36 + 9 + 3 \]<br /><br />Combine the terms:<br />\[ P(-3) = -135 - 36 + 9 + 3 = -135 - 33 + 3 = -135 - 30 = -165 \]<br /><br />Therefore, the value of \( P(c) \) when \( c = -3 \) is:<br />\[ P(-3) = -165 \]