Question

I will fan and medal

Part 1: Suppose you divide a polynomial by a binomial. How do you know if the binomial is a factor of the polynomial? Create a sample problem that has a binomial which IS a factor of the polynomial being divided, and another problem that has a binomial which is NOT a factor of the polynomial being divided.

Answer 1

@campbell_st

Answer 2

you use the factor theorem

if
(x - a) is a factor

then

f(a) = 0

Answer 3

This is for the first question right?

Answer 4

here is a simple example

is (x - 3) a factor of

x^2 - 8x + 15

well find f(3)

f(3) = 9 -24 + 15

f(3) = 0

so

(x - 3) is a factor of the polynomial

Answer 5

for the not question show

(x - 2) isn't a factor

f(2) = 4 - 16 + 15
= 3

so not a factor

Answer 6

@campbell_st so is there a way to put this question in a simple answer?

Answer 7

@phi plz help

Answer 8

go and google the factor theorem... that is what you are being asked about

here is the basics

if

(x - a) is a factor of a polynomial P(x)

then x - a = 0 or x = a is zero of the polynomial.

by substituting x = a into the polynomial... and getting P(a) = 0..

you are showing that there is no remainder, when the division occurs so (x - a) is a factor.

Answer 9

But @campbell_st so the question How do you know if the binomial is a factor of the polynomial?is by using the factor theorem?

Answer 10

help @phi?

Answer 11

How do you know if the binomial is a factor of the polynomial?

Have you learned how to divide a binomial into a polynomial?

Answer 12

i dont know but it would be great if u showed me plz

Answer 13

Let me ask it this way:

were you supposed to learn how to divide a binomial into a polynomial?

Answer 14

or were you taught synthetic division?

or were you taught the factor theorem that campbell mentioned?

those are 3 ways to tell if a binomial divides evenly into a polynomial

Answer 15

yes i am going to 9th and this is just a review of algebra 1 B

Answer 16

which sounds most familiar?

Answer 17

Here is how to divide a polynomial by a binomial
http://www.khanacademy.org/math/algebra2/polynomial_and_rational/dividing_polynomials/v/dividing-polynomials-1

Answer 18

How do you know if the binomial is a factor of the polynomial?

one answer is use the factor theorem as posted above.
another answer is divide the binomial into the polynomial and see if you get NO remainder

Answer 19

Create a sample problem that has a binomial which IS a factor of the polynomial

to do this, first write down 2 binomials, and multiply them together
(both of your binomials are factors of the polynomial)

Answer 20

So for the first question i could put umm is
You can tell if the binomial is a factor of the polynomial is with the Factor Theorem,and Synthetic Division?

Answer 21

If you explain the factor theorem
or
if you say, after using synthetic division you get a remainder of zero

Answer 22

ok so
lets just say i was answering this question(which i am)

I would start like
The way you can tell if the binomial is a factor of the polynomial is if you use the synthetic division and get a remainder of zero.

Answer 23

Then i would give a example

Answer 24

that would be good.

Can you find a sample problem?

Answer 25

Um i made 1

Answer 26

(2x-7)(5x+3)

Answer 27

so i would use FOIL method right?

Answer 28

@phi i gave a sample would this be good?