Question

Check whether x-1 is a factor of x3-3x2+3x-1

Answer 1

Answer:

x³-3x²+3x-1

(x³-1)-3x(x-1)

yes x-1 is a factor of x³-3x²+3x-1

Answer 2

Answer:

Answer:for checking that whether a polynomial or number is a factor of another polynomial or another number the number or polynomial must divide the polynomial or number completely

Step-by-step explanation:

Method 01:

Substitution method:

$x - 1 = 0|$

$therefore \: \: \: \: \: \\ x = 0 - + 1$

$x = 1$

now substituting value of x in the polynomial:

$p(x) = {x}^{3} - 3 {x}^{2} + 3x - 1 \\ thus \\ p(1) = {1}^{3} - 3 \times {1}^{2} + 3 \times 1 - 1$

$p(1) = 1 - 3 + 3 - 1$

$p(x) = 1 - 1 + 3 - 3$

$p(x) = 0$

Therefore x-1 is a factor of the given polynomial

method 02:

direct division method:

pls see the picture of method 2 attached to the answer!

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