Question

use factor theorem to show that (x-3) is a factor of x^3-3 x^2+4 x-12

Answer 1

Given polynomial p(x) = x³ - 3x² +4x - 12
If x-3 is a factor of p(x) then... p(3) =0
p(3) = 3³ - 3(3)² +4(3) - 12
= 27 - 27 + 12 - 12
= 0
So p(3) = 0.
Hence, x-3 is a factor of p(x).

Answer 2

$\huge\underline\bold{\purple{\fbox{SOLUTION}}}$

Given is that . Prove that x - 3 is a factor of polynomial $x^3\:-\:3x^2\:-\:4x\:-\:12$

If x - 3 would be a factor of this given polynomial then ,

g (x) = x - 3 = 0

x = 3

Substituting the value 3 of the variable x in the polynomial $x^3\:-\:3x^2\:-\:4x\:-\:12$

$\implies\:p(x)\:=\:x^3\:-\:3x^2\:-\:4x\:-\:12$

$\implies\:p(x)\:=\:(3)^3\:-\:3(3)^2\:-\:4(3)\:-\:12\:=\:0$

$\implies\:p(x)\:=\:\:27\:-\:27\:+\:12\:-\:12\:=\:0$

[$\implies\:p(x)\:=\:0\:=\:0$

Hence , LHS = RHS

Thus proved that x - 3 is a factor of the polynomial $x^3\:+\:3x^2\:-\:4x\:-\:12$

$\huge\star\:\:{\orange{\underline{\blue{\mathbf{Basics}}}}}$

Factorising is may be the most important concept in maths . Knowing how to factorise can be really helpful for us . Some important steps or tips while factorising are mentioned below

• A common method of factor rising is to completely factor The number into its positive factors .

• Taking out the greatest common factor can also be one way to do factorising

• The most important thing by factorising is to know the common and basic algebraic formulas .