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

[tex]\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[/tex]

bhoopendrasisodiya34 bhoopendrasisodiya34 · Answer 2 · 2022-02-19T06:10:50+01:00

The value of c so that (x-2) is a factor of the polynomial p(x), should satisfy the polynomial at x equal to 2. The value of c is 2.

What is polynomial equation?

A polynomial equation is the equation in which the unknown variable is one and the highest power of the unknown variable is n.

Here, n is any real number.

Given information-

The given polynomial in the problem is

[tex]p(x)=x^3-4x^2+3x+c[/tex]

One factor of the given polynomial is (x-2).

In the given problem the highest power of the polynomial is 3.

As one of the factor of the given polynomial is (x-2). Thus it must satisfy the polynomial at, x equal to 2.

Put the value in the above equation as,

[tex]p(2)=(2)^3-4(2)^2+3(2)+c=0[/tex]

Solve it further,

[tex]8-4\times4+3\times2+c=0\\8-16+6+c=0\\-2+c=\\c=2[/tex]

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

Learn more about the polynomial equation here;

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