Q.If $x^2+x+1$ is a factor of the polynomial $3x^3+8x^2+8x+a$, then find the value of $a$.

Step 1. Divide $3x^3+8x^2+8x+a$ by $x^2+x+1$: $3x^3\div x^2=3x$; $3x(x^2+x+1)=3x^3+3x^2+3x$.

Step 2. Subtract: $(3x^3+8x^2+8x+a)-(3x^3+3x^2+3x)=5x^2+5x+a$.

Step 3. Continue: $5x^2\div x^2=5$; $5(x^2+x+1)=5x^2+5x+5$. Subtract: $(5x^2+5x+a)-(5x^2+5x+5)=a-5$. …

• Stopping the division one step early and reading off the wrong remainder. …