Find the value of c so that (x+3) is a factor of the polynomial p(x). p(x)=x^(3)-4x^(2)+cx+33 c=

Factor Theorem Application: If (x+3) is a factor of p(x), then p(-3) must equal 0 according to the Factor Theorem. Let's calculate p(-3). p(-3) = (-3)^(3) - 4(-3)^(2) + c(-3) + 33Calculate p(-3): Now, let's substitute the values and simplify the expression. p(-3) = (-27) - 4(9) - 3c + 33 p(-3) = -27 - 36 - 3c + 33Substitute and Simplify: Combine like terms to simplify further. p(-3) = -27 - 36 + 33 - 3c p(-3) = -30 - 3cCombine Like Terms: Since p(-3) must be 0 for (x+3) to be a factor, we set the equation equal to 0 and solve for c. 0 = -30 - 3cSet Equation Equal to 0: Add 30 to both sides of the equation to isolate the term with c. 3c = 30Isolate and Solve for c: Divide both sides by 3 to solve for c. c = 30 / 3 c = 10

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Find the value of
c so that
(x+3) is a factor of the polynomial
p(x).

p(x)=x^(3)-4x^(2)+cx+33

c=

Find the value of $c$ so that $(x+3)$ is a factor of the polynomial $p(x)$ . $\newline$ $p(x)=x^{3}-4 x^{2}+c x+33$ $\newline$ $c=$

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Math Problems

Algebra 2

Composition of linear and quadratic functions: find a value

Full solution

Q. Find the value of

c

so that

(x+3)

is a factor of the polynomial

p(x)

\newline

p(x)=x^{3}-4 x^{2}+c x+33

\newline

c=

Factor Theorem Application: If $(x+3)$ is a factor of $p(x)$ , then $p(-3)$ must equal $0$ according to the Factor Theorem. $\newline$ Let's calculate $p(-3)$ . $\newline$ $p(-3) = (-3)^{3} - 4(-3)^{2} + c(-3) + 33$
Calculate $p(-3)$ : Now, let's substitute the values and simplify the expression. $p(-3) = (-27) - 4(9) - 3c + 33$ $p(-3) = -27 - 36 - 3c + 33$
Substitute and Simplify: Combine like terms to simplify further. $\newline$ $p(-3) = -27 - 36 + 33 - 3c$ $\newline$ $p(-3) = -30 - 3c$
Combine Like Terms: Since $p(-3)$ must be $0$ for $(x+3)$ to be a factor, we set the equation equal to $0$ and solve for $c$ . $0 = -30 - 3c$
Set Equation Equal to $0$ : Add $30$ to both sides of the equation to isolate the term with $c$ . $\newline$ $3c = 30$
Isolate and Solve for c: Divide both sides by $3$ to solve for $c$ . $c = \frac{30}{3}$ $c = 10$