# How do you divide (2x^3+28x^2+86x+60)div(x+10) using synthetic division?

Jan 9, 2018

$\left(2 {x}^{3} + 28 {x}^{2} + 86 x + 60\right) \div \left(x + 10\right) = 2 {x}^{2} + 8 x + 6$

#### Explanation:

{: ("row 0:",,color(grey)(x^3),color(grey)(x^2),color(grey)(x^1),color(grey)(x^0)), ("row 1:",,2,28,86,60), ("row 2:",ul(+color(white)("x")),ul(color(white)("xxx")),ul(-20),ul(-10),ul(-60)), ("row 3:",xxcolor(blue)(""(-10)),2,8,6,0), ("row 4:",,color(grey)(x^2),color(grey)(x^1),color(grey)(x^0),color(grey)("R")) :}

rows 0 and 4 are not really part of the synthetic division; they are simply for reference purposes.

row 1 are the coefficients of the terms of the dividend (in cases where the exponent of the variable does not appear in the expression be sure to use $0$)

row 2 is the product of the previous column's value in row 3 times the value required for $x$ to make the divisor ($x + 10$ in this case) equal to $0$.

row 3 is the sum the the values in the corresponding column from rows 1 and 2.

Notice that the exponents of the variable ($x$ in this case) have been reduced by $1$ fro each column; $\textcolor{g r e y}{\text{R}}$ is the remainder.

Jan 9, 2018

Multiply x+10 by $2 {x}^{2} + 8 x + 6$ and get $2 {x}^{3} + 28 {x}^{2} + 86 x + 60$, so the answer is $2 {x}^{2} + 8 x + 6$.

#### Explanation:

x+10 times $2 {x}^{2} + 8 x + 6$= $2 {x}^{3} + 8 {x}^{2} + 6 x + 20 {x}^{2} + 80 x + 60$
which by adding like terms is $2 {x}^{3} + 28 {x}^{2} + 86 x + 60$.