How do you factor #x^3 – 4x^2 +x + 6#?

Answer 1

#(x-2)(x-3)(x+1)#

It is usually really, really hard to factorize a cubic function. However, for this polynomial, we can factor by grouping. We try values for splitting the term #-4x^2#.
For example, we split it into #-2x^2-2x^2#.
The equation becomes this: #(x^3-2x^2)-(2x^2-x-6)#. We can factorize each of the expressions in the parentheses: #x^2(x-2)-(x-2)(2x+3)#. There is a common factor #(x-2)#.
Factoring the common factor out, we get #(x-2)(x^2-2x-3)#. We then factorize #x^2-2x-3# to #(x-3)(x+1)#.
The fully factored form is then #(x-2)(x-3)(x+1)#.
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

#x^3-4x^2+x+6=color(magenta)((x-2)(x-3)(x+1))#

Provided the expression has rational roots, we can use the rational root theorem.

For the expression #color(green)(x^3-4x^2+x+6)#
according to the rational root theorem, possible rational roots are:
#color(white)("XXX"){+-1,+-2,+-3,+-6}#

With the use of a spreadsheet these values can be easily checked (it can also be done with a calculator or even manually with a bit more effort).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 3

To factor the expression x^3 - 4x^2 + x + 6, you can use a variety of factoring methods such as grouping, synthetic division, or the rational root theorem. One possible method is to use grouping:

  1. Group the terms: (x^3 - 4x^2) + (x + 6)
  2. Factor out the greatest common factor from each group: x^2(x - 4) + 1(x - 4)
  3. Factor out the common binomial factor (x - 4): (x - 4)(x^2 + 1)

So, the factored form of x^3 - 4x^2 + x + 6 is (x - 4)(x^2 + 1).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7