Question

divide using long division or synthetic division. remember that (2x^3 + 8x - 19)÷(x - 1)
2x^2 + 2x + 10
suggested tutorial: learn it: divide a polynomial by a binomial of the
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Explanation:

Step1: Set up synthetic division

The divisor is $x - 1$, so we use $c = 1$. Write the coefficients of the dividend $2x^{3}+0x^{2}+8x - 19$ which are $2,0,8,-19$.

Step2: Bring down the first coefficient

Bring down the first coefficient $2$.

Step3: Multiply and add

Multiply $1$ (from $x - 1$) by $2$ to get $2$, add to the second coefficient $0$: $0 + 2=2$. Then multiply $1$ by $2$ to get $2$, add to the third coefficient $8$: $8 + 2 = 10$. Then multiply $1$ by $10$ to get $10$, add to the fourth coefficient $- 19$: $-19+10=-9$.

Step4: Write the quotient and remainder

The quotient is $2x^{2}+2x + 10$ and the remainder is $-9$. So $(2x^{3}+8x - 19)\div(x - 1)=2x^{2}+2x + 10+\frac{-9}{x - 1}$.

Answer:

$2x^{2}+2x + 10+\frac{-9}{x - 1}$