Home > Algebra > Factoring Completely

How do you factor #8x^3-4x^2-2x+1#?

Answer 1

Avery Alexander

#8x^3-4x^2-2x+1=(2x-1)(2x+1)(2x-1)#

Factor by grouping and using the difference of squares identity:

#a^2-b^2 = (a-b)(a+b)#

with #a=2x# and #b=1# as follows:

#8x^3-4x^2-2x+1#

#=(8x^3-4x^2)-(2x-1)#

#=4x^2(2x-1)-1(2x-1)#

#=(4x^2-1)(2x-1)#

#=((2x)^2-1^2)(2x-1)#

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

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

Answer 2

Jameson Allen

To factor (8x^3 - 4x^2 - 2x + 1), you can use techniques like grouping or factoring by grouping. However, this polynomial does not have any common factors among its terms or any obvious factoring patterns. Therefore, you may need to use more advanced techniques such as the Rational Root Theorem or synthetic division to find the roots or factors. Once you find a root or factor, you can use polynomial division or synthetic division to divide the polynomial by that factor and continue factoring.

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

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.