Question

Is x-3 is a factor of x^3- 3x^2 +4x -12?

Answer 1

QUESTION:

Is x-3 is a factor of x^3- 3x^2 +4x -12?

TO FIND :

(x-3) is a factor of given polynomial or not?

ANSWER:

If we put x = 3 in the polynomial and the value of the polynomial we get 0 then (x-3) is factor of given polynomial.

so,

$p(3) = {3}^{3} - 3 \times {3}^{2} + 4 \times 3 - 12 \\ p(3) = 27 - 3 \times 9 + 12 - 12 \\ p(3) = 27 - 27 + 0 \\ p(3) = 0$

$\huge\orange {p(3) = 0}$

Hence it is a factor of given polynomial.

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Answer 2

Answer:

if x-3 is a factor of x^3-3x^2+4x-12 then it will satisfy the equation

$p(x) = {x}^{3} - 3 {x}^{2} + 4x - 12$

$p(3) = {3}^{3} - 3({3})^{2} + 4(3) - 12$

$= 27 - 27 + 12 - 12$

$= 0$

$x - 3 \: is \: a \: factor \: of \: p(x)$

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