Question

Ugh. please help me out here. ):

What is the dividend f(x)?

http://roads.advancedacademics.com/coursecontent/math/IIB05/AlgIIB_unit1a_files/image103.jpg

A. 3x^3 - 10x^2 +14x - 7
B. 3x^4 - 10x^3 + 14x^2 - 7
C. 3x^3 - 4x^2 +6x - 5
D. 3x^2 - 4x +6

Answer 1

well, you need the coefficients 3, -10, 14, -7, and you need a sequence of powers of x with no gaps (otherwise there would be zeros in the table). which choice do you think fits?

the dividend is the thing being divided into smaller pieces — it would be the numerator if written as a fraction.

Answer 2

my best guess was A ...

Answer 3

i dont understand algebra, im into english not this nonsense. hah.

Answer 4

shouldn't have to guess, I told you exactly how to find the answer...

Answer 5

i dont know what it means to not have these gaps,

Answer 6

we can rule out C and D because they don't have the right numbers. the only question is whether \[3x^3-10x^2+14x-7\](A) or \[3x^4-10x^3+14x^2-7\](B)
is the right answer. The table in synthetic division requires you to write 0 wherever there is a missing term. \(3x^4-10x^3+14x^2-7\) is missing the \(x\) term — for synthetic division purposes, it must be written as \[3x^4-10x^3+14x^2+0x-7\] Otherwise it is equivalent to trying to divide 105 by 5 by writing 5 | 15 (skipping the 0 in the 10s place)

Answer 7

Does that make sense now?

Answer 8

not really, and now i just feel stupid all over again.

Answer 9

i was never taught these things, so i just sit here and stare and cant make sense of it. im sorry for wasting your time. =/

Answer 10

okay. let's try a different way. for the synthetic division to work, you have to list all of the terms from the highest power of x down to the constant term (the number).

Answer 11

you're not wasting my time.

Answer 12

so, you look at your polynomial, and you write it in descending order of the exponents. if there are any numbers that you skip over in the exponents, counting down from the highest one to just plain old x, then you need to put in a term with a 0 coefficient there. It doesn't change the value of the polynomial AT ALL, so that's why we usually don't bother writing them out, but here we need to account for them. Just like $105 must be written with that 0 in the 10s place, even though there are no 10s involved.

Answer 13

A few examples:
\[x^2+2x+1\] no gaps, because the highest exponent is 2, and there is an x term (which represents \(x^1)\))
\[x^2+1\]has a gap, the \(x^1\) term is not present, so we would rewrite as \[x^2+0x+1\]
\[x^4+3x^3+2x^2+x+1\]no gaps, all exponents from 4 down to 1 are present (1 is \(x^1 = x\))
\[x^4+2x^2+1\]gap at the \(x^3\) term, gap at the \(x^1\) term, need to rewrite as
\[x^4+0x^3+2x^2+0x+1\]

Now does it make sense?

Answer 14

think of the increasing powers of x as being exactly like the powers of 10 in a decimal number, because that's exactly what they are. each different power of x is a different "place" — there's the 1's place (the constant at the end, if any), there's the \(x\)'s place, there's the \(x^2\)'s place, there's the \(x^3\)'s place, etc...

Answer 15

its starting to make sense to me now.

Answer 16

good!

Answer 17

any more questions about this?

Answer 18

no, i think ive got this now! (: thanks!!

Answer 19

great! good luck with your work...