Question

Find the value of c so that (x-2) is a factor of the polynomial p(x)

Answer 1

Answer:

c = 2

Step-by-step explanation:

$\text{If}\ (x-a)\ \text{is a factor fo polynomial}\ w(x),\ \text{then}\ a\ \text{is a root of plynomial}\ w(x):\\\\w(a)=0.\\\\\text{We have}\\\\\text{the polynomial}\ p(x)=x^3-4x^2+3x+c\\\\\text{the factor of the polyniomial}\ p(x):(x-2)\\\\x=2\ \text{is the root of polynomial}\ p(x).\ \text{Therefore we have the equation:}\\\\2^3-4(2^2)+3(2)+c=0\\8-4(4)+6+c=0\\8-16+6+c=0\\-2+c=0\qquad\text{add 2 to both sides}\\c=2$