Question

for the given polynomial p(x) and the given c, use the remainder theorem to find p(c). p(x)=x³ + 5x² - 6x + 3, 3 p(c)= (simplify your answer )

Explanation:

Step1: Identify c and polynomial

We have $c=3$, $P(x)=x^3+5x^2-6x+3$

Step2: Substitute $x=3$ into $P(x)$

$P(3)=3^3 + 5(3)^2 - 6(3) + 3$

Step3: Calculate each term

$3^3=27$, $5(3)^2=5\times9=45$, $-6(3)=-18$

Step4: Sum all terms

$P(3)=27+45-18+3$

Answer:

$57$