Find the value of c so that (x-2) is a factor of the polynomial p(x). p(x)=x^(3)-4x^(2)+3x+c c=

Factor Theorem: If (x-2) is a factor of p(x), then p(2) must equal 0 according to the Factor Theorem.Substitute x = 2: Substitute x = 2 into the polynomial p(x) = x^3 - 4x^2 + 3x + c. p(2) = (2)^3 - 4(2)^2 + 3(2) + cCalculate p(2): Calculate the value of p(2) using the substitution from the previous step. p(2) = 8 - 4(4) + 3(2) + c p(2) = 8 - 16 + 6 + cSimplify expression: Simplify the expression to find the value of p(2). p(2) = -8 + 6 + c p(2) = -2 + cSet expression equal to 0: Since p(2) must equal 0 for (x-2) to be a factor of p(x), set the expression equal to 0 and solve for c. -2 + c = 0Solve for c: Add 2 to both sides of the equation to isolate c. c = 2

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

p(x)=x^(3)-4x^(2)+3x+c

c=

Find the value of $c$ so that $(x-2)$ is a factor of the polynomial $p(x)$ . $\newline$ $p(x)=x^{3}-4 x^{2}+3 x+c$ $\newline$ $c=$

View step-by-step help

Home

Math Problems

Algebra 2

Composition of linear and quadratic functions: find a value

Full solution

Q. Find the value of

c

so that

(x-2)

is a factor of the polynomial

p(x)

\newline

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

\newline

c=

Factor Theorem: If $(x-2)$ is a factor of $p(x)$ , then $p(2)$ must equal $0$ according to the Factor Theorem.
Substitute $x = 2$ : Substitute $x = 2$ into the polynomial $p(x) = x^3 - 4x^2 + 3x + c$ . $\newline$ $p(2) = (2)^3 - 4(2)^2 + 3(2) + c$
Calculate $p(2)$ : Calculate the value of $p(2)$ using the substitution from the previous step. $\newline$ $p(2) = 8 - 4(4) + 3(2) + c$ $\newline$ $p(2) = 8 - 16 + 6 + c$
Simplify expression: Simplify the expression to find the value of $p(2)$ . $p(2) = -8 + 6 + c$ $p(2) = -2 + c$
Set expression equal to $0$ : Since $p(2)$ must equal $0$ for $(x-2)$ to be a factor of $p(x)$ , set the expression equal to $0$ and solve for $c$ . $\newline$ $-2 + c = 0$
Solve for $c$ : Add $2$ to both sides of the equation to isolate $c$ . $c = 2$