Question

please help:))

Answer 1

You tell me. What are the coefficients of your quotient? Ignore the remainder (0).

Answer 2

2 and 5?

Answer 3

please help:))

Answer 4

well, have you done Systhetic divisions yet?

Answer 5

yes

Answer 6

well... so.. hmm
notice, the remainder is 0
meaning that x+4 is a factor
since dividing by -4 gives a remainder of 0
so, the other factor will be \(\begin{array}{rrrrrrr}
-4&|&1&4&-25&-100\\
&|&&-4&0&100
\\\hline\\
&&{\color{brown}{ 1}}&{\color{brown}{ 0}}&{\color{brown}{ -25}}&{\color{blue}{ 0}}
\end{array}\qquad \qquad {\color{blue}{ remainder}}\)

(x+4)( ? ) what do you think it may be?

Answer 7

is it 25 because dividing -25 remainder of 0?

Answer 8

oh i see -100

Answer 9

soo then it woud be x+100?

Answer 10

notice the original coefficients Avery used
what would the original equation would look like?

Answer 11

or lemme put it differently

if you were to divide, say \(5x^3+3x^2-7x-13\quad \div\quad (x+4)\)
what would be your divisor and dividend for the synthetic division?

Answer 12

the divisor is the x+4 and the dividend is the other one

Answer 13

ok.. so

Answer 14

x+4 on the left and the other one on the right

Answer 15

what do you mean

Answer 16

well... this is a good time to cover your section on synthetic divisions

Answer 17

\[\begin{array}{rrrrrrr} -4&|&1&4&-25&-100\\ &|&&-4&0&100 \\\hline\\ &&{\color{brown}{ 1}}&{\color{brown}{ 0}}&{\color{brown}{ -25}}&{\color{blue}{ 0}} \end{array}\qquad \qquad {\color{blue}{ remainder}}\]

Answer 18

okay is the other factor x+100 or not ?

Answer 19

Here your remainder is zero (0).

The coefficients I asked you to identify are 1, 0 and -25. You are done with the -100.

These coefficients 1, 0 and -25 correspond to the quadratic factor

\[1x^2+0x-25=x^2-25. \]

Answer 20

That's all.
So, what is the answer to this question?

Is it possible to factor x^2-25 further? If so, please do so.

Answer 21

yea so x^2-5