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The polynomial
p(x)=3x^(3)-5x^(2)-4x+4 has a known factor of
(x-2).
Rewrite
p(x) as a product of linear factors.

p(x)=

◻

The polynomial $p(x)=3 x^{3}-5 x^{2}-4 x+4$ has a known factor of $(x-2)$ . $\newline$ Rewrite $p(x)$ as a product of linear factors. $\newline$ $p(x)=$ $\newline$ $\square$

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Find the roots of factored polynomials

Full solution

Q. The polynomial

p(x)=3 x^{3}-5 x^{2}-4 x+4

has a known factor of

(x-2)

.

\newline

Rewrite

p(x)

as a product of linear factors.

\newline

p(x)=

\newline

\square

Perform Polynomial Division: Since $(x - 2)$ is a known factor, let's perform polynomial division to find the other factors. $\newline$ Divide $p(x)$ by $(x - 2)$ using synthetic division or long division.
Set Up Synthetic Division: Set up synthetic division with $2$ as the root: $\newline$ \begin{array}{r|rrrr} 2 & 3 & -5 & -4 & 4 \ & \underline{\quad} & \underline{\quad} & \underline{\quad} & \underline{\quad} \ & 3 & -1 & -6 & 4 \end{array} $\newline$ Multiply $2$ by $3$ and write the result under $-5$ . Add $-5$ and $6$ to get $-1$ . $\newline$ Multiply $2$ by $-1$ and write the result under $-4$ . Add $-4$ and $2$ $1$ to get $2$ $2$ . $\newline$ Multiply $2$ by $2$ $2$ and write the result under $2$ $5$ . Add $2$ $5$ and $2$ $7$ to get $-4$ . $\newline$ Since the remainder is not zero, there's a mistake. Let's correct it.

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