Question

Divide using synthetic division, and write a summary statement in fraction form. 2x^3 +3x^2 +4x - 10/ x+1

Answer 1

do you know how to do synthetic division?

Answer 2

no

Answer 3

idk sorry

Answer 4

ok.... you'd grab the coefficients of the dividend and put them on the right-hand-side
then the divisor will go on the left-hand side

notice that the divisor is x+1, thus x+1 =0 => x= -1
so we'll end up using for our divisor, " -1 " only

so you'd drop the 1st coefficient and multiply the divisor by it, the product goes underneath the next coefficient

Answer 5

\(2x^3 +3x^2 +4x - 10 \div x+1\\ \quad \\
\begin{array}{rrrrrr}
-1&|&2&3&4&-10\\
&|&&-2\\
\hline\\
&&2&1
\end{array}\)

notice we drop the 1st coefficient, that is "2", -1 * 2 = -2, -2 goes underneath the next coefficient, 3

Answer 6

then we sum them up, 3 - 2 = 1 as you can see above

then we again, do the divisor multiplication of the result of the sum
so -1 * 1 = -1
so \(2x^3 +3x^2 +4x - 10 \div x+1\\ \quad \\
\begin{array}{rrrrrr}
-1&|&2&3&4&-10\\
&|&&-2&-1\\
\hline\\
&&2&1&3
\end{array}\)

Answer 7

okay

Answer 8

4 - 1 = 3

again, we multiply the divisor times the sum result, that is -1 * 3 and that will go under the next coefficient.... so what do you get?

Answer 9

-7

Answer 10

anyhow, lemme post it -1 * 3 = -3 so \(\begin{array}{rrrrrr}
-1&|&2&3&4&-10\\
&|&&-2&-1&-3\\
\hline\\
&&2&1&3&-13
\end{array}\)

Answer 11

well, notice is -10, not +10 so, -10 -3 = -13

Answer 12

ohhhhh

Answer 13

so -1 doesn't work ? or is the numbers at the bottom the answer ?

Answer 14

one thing to recall is that the dividend is firstly arranged in descending order, the 3rd power to the far-left and then down to the right, 2nd power, 1st power and then constant

Answer 15

\(\bf 2x^\color{red}{3} +3x^\color{red}{2} +4x^\color{red}{1} - 10 \div x+1\)

Answer 16

that's how the dividend should be arranged for any division really, either long or synthetic

Answer 17

2x2 + x + 3 + (-13/x+1)

2x2 + 5x + 9 + (1/x+1)

2x2 + x - 3 + (13/x+1)

2x2 + 5x + 9 + (-1/x+1)

Answer 18

@jdoe0001

Answer 19

so from \(2x^3 +3x^2 +4x - 10 \div x+1\\ \quad \\
\begin{array}{rrrrrr}
-1&|&2&3&4&-10\\
&|&&-2&-1&-3\\
\hline\\
&&2&1&3&-13
\end{array}\)

we get a quotient, the quotient is those coefficients, with a lesser exponent than the original

and the last number is our remainder

Answer 20

so it would be a?

Answer 21

\({\bf 2x^\color{red}{3} +3x^\color{red}{2} +4x - 10 \div x+1}\\ \quad \\
\begin{array}{rrrrrr}
-1&|&2&3&4&-10\\
&|&&-2&-1&-3\\
\hline\\
&&2&1&3&-13
\end{array}\bf \implies 2x^\color{red}{2}+1x+3+\textit{(remainder here)}\)

notice that our quotient function, has 1 degree less than the original, the original had a degree of 3, our quotient from the division will have 1 less, or 3-1 = 2, so starts off with an exponent of 2