Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the value of
c so that the polynomial
p(x) is divisible by
(x+2).

p(x)=4x^(3)+cx^(2)+x+2

c=

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

View step-by-step help

View step-by-step help

Composition of linear and quadratic functions: find a value

Full solution

Q. Find the value of

c

so that the polynomial

p(x)

is divisible by

(x+2)

.

\newline

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

\newline

c=

Using the Remainder Theorem: To determine the value of $c$ that makes the polynomial $p(x)$ divisible by $(x+2)$ , we can use polynomial long division or synthetic division. However, a simpler method is to use the Remainder Theorem, which states that if a polynomial $f(x)$ is divisible by $(x - k)$ , then $f(k) = 0$ . In this case, since we want $p(x)$ to be divisible by $(x + 2)$ , we set $x = -2$ and solve for $p(-2) = 0$ .
Substituting $x = -2$ : Substitute $x = -2$ into the polynomial $p(x) = 4x^3 + cx^2 + x + 2$ . $\newline$ $p(-2) = 4(-2)^3 + c(-2)^2 + (-2) + 2$
Calculating p( $-2$ ): Calculate the value of $p(-2)$ . $p(-2) = 4(-8) + c(4) - 2 + 2$ $p(-2) = -32 + 4c - 2 + 2$ $p(-2) = -32 + 4c$
Setting $p(-2) = 0$ : Since we want $p(x)$ to be divisible by $(x + 2)$ , we set $p(-2) = 0$ . $\newline$ $-32 + 4c = 0$
Solving for c: Solve for c. $\newline$ $4c = 32$ $\newline$ $c = \frac{32}{4}$ $\newline$ $c = 8$

More problems from Composition of linear and quadratic functions: find a value

Question

Find the inverse of the function.

y = x + 3

Write your answer in the form

ax + b

. Simplify any fractions.

y =

Posted 5 months ago

Question

(r \circ s)(x)

\newline

3

\newline

2

5

\newline

Write your answer as a polynomial in simplest form.

\newline

(r \circ s)(x) =

Posted 7 months ago

Question

(f + g)(x)

\newline

f(x) = -3x

\newline

g(x) = 3x + 1

\newline

\newline

Write your answer as a polynomial or a rational function in simplest form.

\newline

\underline{\hspace{3cm}}

\newline

Posted 7 months ago

Question

(f * g)(x)

\newline

f(x) = -x + 4

\newline

g(x) = 4x

\newline

\newline

Write your answer as a polynomial or a rational function in simplest form.

\newline

\underline{\hspace{3em}}

\newline

Posted 7 months ago

Question

What is the domain of

\left(\frac{f}{g}\right)(x)

\newline

f(x) = 2x

\newline

g(x) = -5x + 3

\newline

\newline

[\text{A]All real numbers}

\newline

[\text{B]All real numbers except } \frac{3}{5}

\newline

[\text{C]All real numbers except } -\frac{3}{5}

\newline

[\text{D]All real numbers except } \frac{5}{3}

Posted 9 months ago

Question

Find the inverse of the function.

\newline

-3x

\newline

Write your answer in the form

ax + b

. Simplify any fractions.

\newline

Posted 7 months ago

Question

(f \circ g)(0)

\newline

f(x) = 6x

\newline

g(x) = x^2 + 4x

\newline

(f \circ g)(0) =

Posted 7 months ago

Question

(f \circ g)(x)

\newline

f(x) = x^2 + 5

\newline

g(x) = 4x

\newline

Write your answer as a polynomial in simplest form.

\newline

(f \circ g)(x) =

Posted 7 months ago

Question

f(x)

the inverse function of

g(x)

\newline

f(x) = x

\newline

g(x) = -4x

\newline

\newline

\text{[yes]}

\newline

\text{[no]}

Posted 7 months ago

Question

(f * g)(x)

f(x) = 3x^2 + 9x

g(x) = 3x

Write your answer as a polynomial or a rational function in simplest form. ______

Posted 5 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant