help with factoring by grouping

[lsosa02]

i would appreciate anyones help with this problem . Thank you.

the problem is: acx^m+n+adx^n+bcx^m+bd

the directions say to factor this into two groups . To assume that a,b,c and dare constants . Then it says to varify the factorization by multipliying .

[/u]

 

[Gene]

acx^(m+n)+adx^n+bcx^m+bd
Grouping as
ax^n*(cx^m+d)+b(cx^m+d)
It factors into
(ax^n+b)(cx^m+d)

 

[soroban]

Hello, lsosa02!

How about using parentheses and spaces?
It's really difficult to guess what you meant . . .

Factor: $\displaystyle acx^{m+n}\,+\,adx^n\,+\,bcx^m\,+\,bd$

The directions say to factor this into two groups and assume that a,b,c and dare constants.
Then it says to varify the factorization by multipliying.

Factor the first two terms: $\displaystyle \,acx^{m+n}\,+\,adx^n$
They have a common factor: $\displaystyle \,ax^n$
Factor it out: $\displaystyle \,ax^n(cx^m\,+\,d)$

Factor the last two terms: $\displaystyle \,bcx^m\,+\,bd$
They have a common factor: $\displaystyle \,b$
Factor it out: $\displaystyle \,b(cx^m\,+\,d)$

We have: $\displaystyle \,ax^n(\underbrace{cx^m\,+\,d})\,+\,b(\underbrace{cx^m\,+\,d})$
. . . . . . . . Do you see the common factor?

Factor it out: \(\displaystyle \cx^m\,+\,d)\,(ax^n\,+\,b)\;\;\) . . . There!

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Check

Multiply it out ("FOIL") . . .

We have: $\displaystyle \,(cx^m\,+\,d)(ax^n\,+\,b)$

$\displaystyle \;\;\;=\;(cx^m)(ax^n)\,+\,(cx^m)(b)\,+\,(d)(ax^n)\,+\,(d)(b)$

$\displaystyle \;\;\;=\;acx^{m+n}\,+\,bcx^m\,+\,adx^n\,+\,bd\;\;$ . . . check!

 

[lsosa02]

Thank you both very much . I understand the problem now .