My name is Louise,
the question is a Secondary(10-12) level,
I am a student.

x3 + 9x2 - 7x - 63

Hi Louise,

The only way that I know to factor a cubic is to look for patterns and groupings. The first observation I make with this problem is that 7, 9 and 63 appear and 7 x 9 = 63. Thus

x3 + 9x2 - 7x - 63 = x3 + 9x2 - 7(x + 9)

Can you see what to do next?
Penny

Hello,
there is a certain way I'm suppose to be factoring the question! I will show you with one of the questions I have already done.

a2 - 4b2 - 2a + 1
=(a2 - 2a + 1) - 4b2
=(a - 1)(a - 1) - 4b2
=(a - 1)2 - 4b2
=[(a - 1) - 2b][(a - 1) + 2b]
=(a - 1 - 2b)(a - 1 + 2b)
Thank You Again, I hope you can help me:)

Hi again Louise,

I think the point in both problems is that you break the problem into pieces that you can factor, factor the pieces and then see if you can put them together again. In the problem that you solved you factored a2 - 2a + 1 as (a - 1)2 and then saw (a - 1)2 - 4b2 as a difference of squares.

In the problem you sent us, x3 + 9x2 - 7x - 63, first factor -7x - 63,

-7x - 63 = -7(x + 9)
and then factor x3 + 9x2,

x3 + 9x2 = x2(x + 9)
Hence

x3 + 9x2 - 7x - 63
= x2(x + 9) -7(x + 9)
= (x2 - 7)(x + 9)

Penny
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