Question

divide by using synthetic division. simplify your answer as much as possible.
$(y^{2}-5y + 4)\div(y - 4)=\square$

Explanation:

Step1: Identify root of divisor

For $y-4=0$, the root is $y=4$.

Step2: List coefficients of dividend

Dividend $y^2-5y+4$ has coefficients $1, -5, 4$.

Step3: Perform synthetic division

Bring down 1. Multiply by 4: $1\times4=4$. Add to -5: $-5+4=-1$.
Multiply -1 by 4: $-1\times4=-4$. Add to 4: $4+(-4)=0$.

Step4: Write quotient and remainder

The first two results are coefficients of the quotient: $1y - 1$, remainder is 0.

Answer:

$y - 1$