factor the polynomial

Question

4m^2-8m^3-49n^2+343n^3

Answer 1

Hi Kelly;

4m²-8m³-49n²+343n³

I would break this down into two separate equations...

FIRST HALF******************************************

4m²-8m³

We need the factor-able equation to be as simple as possible.

Therefore...

4(m²-2m³)

Then...

4m(m-2m²)

 

4m(      m)(     m)

We know that one of the parenthetical equations must be subtraction to yield the result of -2m².

We also know that one of the m's in either parenthetical equation must be multiplied by 2.

4m(    -2m)(    +m)   or   4m(    +2m)(    -m)

We also know that when we execute FOIL, the First must yield 0 because there is no free-standing number in the original equation. Henceforth, one of the parenthetical numbers must be zero.

Through trial and error, we complete this...

4m(0+m)(1-2m)

FOIL...

FIRST.....4m(0)(1)=0

OUTER....4m(0)(-2m)=0

INNER....4m(m)(1)

LAST......4m(-2m²)

TOTAL....4m(m-2m²)

 

SECOND HALF**********************************

-49n²+343n³

(Please note the negative at the beginning.  It would be very easy to forget that while working under the pressures of an exam.)

Our next priority is to see what 49 and 343 have in common.

49 X 7=343

Let's simplify the original equation...

-49(n²-7n³)

(Note that when I removed the negative from the equation, n² became positive, and n³ became negative.)

Let's proceed to simplify...

-49n(n-7n²)

-49n(0+n)(1-7n)

FOIL...

FIRST.....49n(0)(1)=0

OUTER....49n(0)(-7n)=0

INNER.....49n(n)(1)=n

LAST.......49n(n)(-7n)=-7n²

TOTAL.....49n(n-7n²)

Answer 2

Hey Kelly -- we may extract common elements ==> 4m*m(1-2m) + 49n*n(7n-1)

Best wishes :)