Factoring Questions in Algebra 2 Trig?

Question

Okay... so I get the jist of factoring...blablabla BASIC

But yea, need help with two problems

How to factor:

(x-1)3 - (x-1)2 (that is (x-1) to the third - (x-1) to the second)

and

(z-4)3-4(z-4) (that is z-4 to the third minus 4 times the quantity x-4

HELP!!!

Answer 1

First of all, Ms. Softball, use a carat "^" to show an exponent. Save you time-saves me confusion.

As for factoring, if you see a COMMON term in the problem, you can factor "out" that term up to the lowest exponent that it has. Factoring is a type of division simplification. For example, in the first problem (x-1)^3 - (x-1)^2, you see (x-1), the
common term. You can factor "out" (x-1)^2 as a factor. If you divided by (x-1)^2, you would have left in the numerator (x-1) - 1, which is x-2. So here you have (x-1)^2 (x-2)

Once we have done that, just following the bouncing ball in the second problem.

Answer 2

It's like factoring a^3 - a^2 into a^2(a-1)
So (x-1)^2 [(x-1) - 1]
(x-1)^2 (x-2)

Answer 3

do you mean to the power 3 or to the power (1/3) ???

Answer 4

think of of it as a quadratic in ok^2 and factorise (4k^2-a million)(ok^2+4) if it facilitates replace x = ok^2 so expression substitute into 4x^2+15x-4 first bracket could be extra factorised (distinction of two squares) and additionally you get (2k-a million)(2k+a million)(ok^2+4)