Question

help understanding lesson in writing polynomials in factored form.

Answer 1

so..hmm what part... is throwing you off?

Answer 2

the part after finding the product of ac. I not sure where the number goes or where 4 went.
all the numbers are just confusing me.
*the area I circled.

Answer 3

\(\bf 2x^3-8x^2+6x\implies 2x(x^2-4x^2+6)\impliedby here?\)

Answer 4

I "hate" the way I can't see this guy. @jdoe0001

Answer 5

I've been eating glass lately, thus =)
well, not really, glass is not as tasty anyway

Answer 6

no, the 2x(x^2-3x-x+3) and the stuff below that.

Answer 7

ok

Answer 8

hmm

Answer 9

\(\begin{array}{llll}
2x(x^2-3x-x+3)\\
2x[(x^2-3x)-x+3]\\
2x[(x^2-3x)+(-x+3)]&
\begin{array}{llll}
-x\to -1\cdot x\to &-x\\
+3\to -1\cdot -3\to &+3
\end{array}\\
2x[(x^2-3x)-(x-3)]
\end{array}\)

how about that part?

notice -x+3
if we use say -1*(x-3)
we end up with -(x-3) -> -x + 3

which is the same expression
so we can write -x+3 as -(x-3)
since once expanded, is the same

Answer 10

okay:)

Answer 11

\(\begin{array}{llll}
2x(x^2-3x-x+3)\\
2x[(x^2-3x)-x+3]\\
2x[(x^2-3x)+(-x+3)]\\
2x[(x^2-3x)-(x-3)]\\
2x[{\color{brown}{ x(x-3)}} -(x-3)]\impliedby {\color{brown}{ \textit{common factor of "x"} }}\\
2x[ x{\color{blue}{ (x-3) }} -{\color{blue}{ (x-3) }}]\impliedby {\color{blue}{ \textit{notice the common factor, is a binomial} }}\\
2x[ x{\color{blue}{ (x-3) }} -1{\color{blue}{ (x-3) }}]\\
2x[x{\color{blue}{ (x-3)}}(x-1)]
\end{array}\)

Answer 12

you could see it this way
say (x-3) = a
then

2x(x"a" - 1"a") <--- common factor "a"
2x( "a" (x-1) )

a = (x-3)
thus
2x[ (x-3)(x-1) ]

Answer 13

common factors, don't necessarily have to be a term, or a polyomial
could be anything, so long is "common" to both terms
couild be a fraction
a whole polynomial
a root
a whole expression

Answer 14

common factor simply means
what's common to "all involved sides"
take away that common part
and leave the "different" parts in