Please show all the steps and explain each of the step, thanks in advance
also factor (x^4-x^3-x^2-x) if u have time thankx
also factor (x^4-x^3-x^2-x) if u have time thankx
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x^5-x^4-x+1
Group:
(x^5 - x^4) - (x - 1)
Factor out the common factor:
x^4 (x - 1) - (x - 1)
Use the distributive property:
(x - 1) (x^4 - 1)
Use the rule for factoring the difference of squares:
(x - 1) (x^2 + 1) (x^2 - 1)
Use the same rule again:
(x - 1) (x^2 + 1) (x + 1) (x - 1)
x^4-x^3-x^2-x
Factor out the common factor:
x (x^3 - x^2 - x - 1)
What remains in parentheses doesn't factor any farther, so you're finished.
x^3-5x^2+2x+8
Look at the graph or use the rational roots theorem to find the roots at x = -1, x = 2, and x = 4.
Use the factor theorem to convert these roots into factors:
(x + 1) (x - 2 ) (x - 4)
Group:
(x^5 - x^4) - (x - 1)
Factor out the common factor:
x^4 (x - 1) - (x - 1)
Use the distributive property:
(x - 1) (x^4 - 1)
Use the rule for factoring the difference of squares:
(x - 1) (x^2 + 1) (x^2 - 1)
Use the same rule again:
(x - 1) (x^2 + 1) (x + 1) (x - 1)
x^4-x^3-x^2-x
Factor out the common factor:
x (x^3 - x^2 - x - 1)
What remains in parentheses doesn't factor any farther, so you're finished.
x^3-5x^2+2x+8
Look at the graph or use the rational roots theorem to find the roots at x = -1, x = 2, and x = 4.
Use the factor theorem to convert these roots into factors:
(x + 1) (x - 2 ) (x - 4)