# Thread: Divide 4x^3 + 2x^2 + 10x - 7 by (x-5).

1. ## Divide 4x^3 + 2x^2 + 10x - 7 by (x-5).

divide 4x^3 + 2x^2 + 10x - 7 by (x-5) using the long division..

this is polynomial method i think :/.. help please me.. i thought you will understand me.. thanks.. need the answer right now because i will pass this tommorow.. thanks

2. Are you asking to simplify

$\displaystyle{\frac{4x^3 + 2x^2 + 10x - 7}{x-5}}$?

3. A simple way to write "x raised to the 3 power" is x^3.

In any case, x divides into 4x^3 4x^2 times. Multiplying all of x- 5 by 4x^2 and subtracting, 4x^3+ 2x^2+ 10x- 7- (4x^2- 20x^2)= 22x^2+ 10x- 7.

x divides into 22x^2 22x times. Multiplying all of x- 5 by 22x and subtracting, 22x^2+ 10x- 7- (22x^2- 110x)= 120x- 7.

x divides into 120x 120 times. Multiplying all of x- 5 by 120 and subtracting, 120x- 7- (120x- 600)= 593.

x- 5 divides into 4x^3+ 2x^2+ 10x- 7 gives a quotient of 4x^2+ 22x+ 120 with a remainder of 593.

4. primo candidate for synthetic division ...

Code:
5].......4.......2.......10.......-7
.................20......110.....600
---------------------------------------
.........4.......22......120.....593
quotient ... $4x^2 + 22x + 120 + \frac{593}{x-5}$

5. Or let:

$\displaystyle \frac{4x^3 + 2x^2 + 10x - 7}{x-5} = (ax^2+bx+c)+\frac{r}{(x-5)}$

$\displaystyle \Rightarrow 4x^3 + 2x^2 + 10x - 7 = (x-5)(ax^2+bx+c)+r$

$\displaystyle \Rightarrow 4x^3 + 2x^2 + 10x - 7 = ax^3+(b-5 a)x^2+(c-5 b)x-5c+r$.

Comparing the coefficients:

$\displaystyle a = 4$, $b-5a = 2 \Rightarrow b = 22$, $c-5b = 10 \Rightarrow c = 120$

and finally the remainder $-5c+r = -7 \Rightarrow r = 593$.

So $\displaystyle \frac{4x^3 + 2x^2 + 10x - 7}{x-5} = (4x^2+22x+120)+\frac{593}{x-5}$

6. Hello, ejaykasai!

$\text{Divide }4x^3 + 2x^2 + 10x - 7\text{ by }(x-5)\text{ using long division.}$

You want Long Division? . . . Here it is . . .

. . $\begin{array}{cccccccccc}
&&&& 4x^2 &+& 22x &+& 120 \\
&& -- & -- & -- & -- & -- & -- & -- \\
x-5 & | & 4x^3 &+& \;\;2x^2 &+& 10x &-& 7 \\
&& 4x^3 &=& 20x^2 \\
&& -- & -- & -- \\
&&&& 22x^2 &+& \;\;10x \\
&&&& 22x^2 &-& 110x \\
&&&& -- & -- & -- \\
&&&&&& 120x &-& \;\;\;7 \\
&&&&&& 120x &-& 600 \\
&&&&&& -- & -- & -- \\
&&&&&&&& 593
\end{array}$