Create a quadratic polynomial function f(x) and a linear binomial in the form (x − a).

Part 1. Show all work using long division to divide your polynomial by the binomial.

Part 2. Show all work to evaluate f(a) using the function you created.

Part 3. Use complete sentences to explain how the remainder theorem is used to determine whether your linear binomial is a factor of your polynomial function

Question

Create a quadratic polynomial function f(x) and a linear binomial in the form (x − a).

Part 1. Show all work using long division to divide your polynomial by the binomial.

Part 2. Show all work to evaluate f(a) using the function you created.

Part 3. Use complete sentences to explain how the remainder theorem is used to determine whether your linear binomial is a factor of your polynomial function

oswaldmurphy · Answer

@agent0smith

oswaldmurphy · Answer

@partyshotz2409 @sammixboo  @.Sam.

oswaldmurphy · Answer

@mathmate

will.h · Answer

okay so let's start with making a quadratic polynomials. shouldn't be too hard. let's say 
$$x^4 -5x^2 + 6$$

And a binomial linear $$2x - 4$$

now let's answer the 1st part. we should divide. 
$$(x^4 -5x^2 + 6)/(2x-4)$$
Can you divide?

oswaldmurphy · Answer

I can normally, but I always mess up on this. I do something wrong every time.

will.h · Answer

okay. it's fine i'll help you finish this. but let's make it easier. in the binomial we created let's make it $$x^2 - 2$$ instead of the original. so now we will divide
$$(x^4 -5x^2 + 6)/x^2 - 2$$ Okay so division is so easy. we simply deal with the exponents. so let's divide the 1st term $$x^4/x^2$$ since it is division that means we will subtract exponents that's all. 4 - 2 will equal 2 and therefore the 1st term after division would be $$x^2$$ Now do the same to the rest terms and i will check your answer.

oswaldmurphy · Answer

x^2 - 5 + 6 ?

will.h · Answer

Good job. am confused a little about what should we do to the -2 back in the division system. am guessing to divide the same terms like 6/-2

will.h · Answer

@agent0smith Can you help completing this.

oswaldmurphy · Answer

or @mathmate

will.h · Answer

They both great

mathmate · Answer

The question says linear binomial.
So the denominator would be in the form, say, x-3.
Assume 
$f(x)=x^4+2x^3-x^2+3$
Can you do the division
f(x)/(x-3),
according to what @Will.H showed you?
Long division is a must, both in algebra and everyday math.

oswaldmurphy · Answer

I dont want to sound rude, Im in a HUGE hurry. This is my last question, can you please help me get the answer fast?

will.h · Answer

@mathmate we just divide the identical terms on each other right? like x^4/x and 3/-3 ?

mathmate · Answer

Yep, exactly the way you proceeded, I just changed the denominator to a linear binomial.
I can get it started.|dw:1470514856002:dw|
to be completed