Question

100 points

Can someone help me with this problem, and can you please show me your work so I know how you did it?

Please factor this polynomial completely

18x^3 + 6x^2y - 9x^2 - 3xy

Answer 1

STEP
1
:

y
Simplify —
3
Equation at the end of step
1
:

y
(((18•(x5))•(y3))+((6•(x2))•(y4)))+((((24•(x6))•—)•x)•y)
3
STEP
2
:

Equation at the end of step
2
:

y
(((18•(x5))•(y3))+((6•(x2))•(y4)))+((((23•3x6)•—)•x)•y)
3
STEP
3
:

Canceling Out:

3.1 Canceling out 3 as it appears on both sides of the fraction line


Equation at the end of step
3
:

(((18•(x5))•(y3))+((6•(x2))•(y4)))+((8x6y•x)•y)
STEP
4
:

Equation at the end of step
4
:

(((18•(x5))•(y3))+((2•3x2)•y4))+8x7y2
STEP
5
:

Equation at the end of step
5
:

(((2•32x5) • y3) + (2•3x2y4)) + 8x7y2
STEP
6
:

STEP
7
:
Pulling out like terms

7.1 Pull out like factors :

8x7y2 + 18x5y3 + 6x2y4 = 2x2y2 • (4x5 + 9x3y + 3y2)

Trying to factor a multi variable polynomial :

7.2 Factoring 4x5 + 9x3y + 3y2

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Final result :
2x2y2 • (4x5 + 9x3y + 3y2)