The factors of x^3 -4x^2 -x+4 are?
How do I solve this?
use grouping
x^2(x-4) -1(x-4)
= ....
take it from there.
I do not understand how you grouped the numbers?
expand my answer,
will you not get the original?
so, can I not reverse the process?
btw, my next step would be
(x-4)(x^2 - 4)
= (x-4)(x+1)(x-1)
x^3 -4x^2 -x + 4.
The expression has 4 terms. Therefore,
we can form 2 groups with 2 factorable terms in each group:
(x^3 - x) + (-4x^2 + 4),
Factor each pair:
x(x^2 - 1) -4(x^2 - 1),
Factor out (x^2 - 1):
(x^2 - 1)(x - 4),
(x + 1)(x - 1)(x - 4).
NOTE: (X^2 - 1) = (x + 1)(x - 1)
To find the factors of a polynomial, you need to factorize it. Here's how you can solve this:
1. Start by looking for any common factors that can be factored out. In this case, there are no common factors among the terms.
2. Next, try to identify any patterns or specific techniques that can be applied. In this polynomial, there doesn't seem to be an immediate pattern or any suitable factoring techniques.
3. If no patterns or techniques are apparent, you can use the general technique of factoring by grouping. Here's how it works:
a. Group pairs of terms that have common factors. You can start by pairing the first two terms and the last two terms.
x^3 - 4x^2 - x + 4
Group 1: (x^3 - 4x^2)
Group 2: (-x + 4)
b. Factor out the greatest common factor from each group. In Group 1, the common factor is x^2, and in Group 2, the common factor is -1.
Group 1: x^2(x - 4)
Group 2: -1(x - 4)
c. Notice that both groups have a common factor of (x - 4). Factor out (x - 4) from both groups.
(x^2 - 1)(x - 4)
4. Simplify further if possible. The expression (x^2 - 1) can be factored using the difference of squares formula, which states that a^2 - b^2 = (a + b)(a - b). In this case, a = x and b = 1.
(x^2 - 1) = (x + 1)(x - 1)
5. Therefore, the final factored form of x^3 - 4x^2 - x + 4 is:
(x + 1)(x - 1)(x - 4)
The factors of the polynomial x^3 - 4x^2 - x + 4 are (x + 1), (x - 1), and (x - 4).