Question

Show that (X+3) is a factor of x^3+x^2-4x+6

Answer 1

Step-by-step explanation:

g(x)=x+3=0

g(x)=(-3)

p(x)=x³+x²-4x+6

p(-3)=(-3)³+(-3)²-4(-3)+6=0

-27+9+12+6=0

-27+27=0

0=0

LHS=RHS

∴ (x+2) is a factor of x³+x²-4x+6.

Answer 2

$\huge\star\:\:{\orange{\underline{\green{\mathbf{Answer}}}}}$

Given is that . Prove that x + 3 is a factor of polynomial $x^3\:+\:x^2\:-\:4x\:+\:6$

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 $x^3\:+\:x^2\:-\:4x\:+\:6$

$\implies\:p(x)\:=\:x^3\:+\:x^2\:-\:4x\:+\:6$

$\implies\:p(x)\:=\:(-3)^3\:+\:(-3)^2\:-\:4(-3)\:+\:6\:=\:0$

$\implies\:p(x)\:=\:-\:27\:+\:9\:+\:12\:+\:6\:=\:0$

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

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

Hence , LHS = RHS

Thus proved that x+ 3 is a factor of the polynomial $x^3\:+\:x^2\:-\:4x\:+\:6$

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

While solving any question related to polynomial use four-step strategy .

• Simplify both sides if you think it's required

• write the equation in standard form

• Factorise the equation

• Zero - Product Principle or LHS = RHS