Problem

The Remainder Theorem
If
the polynomial P(x) is divided by (x - ). the remainder R is a
constant and is equal to P().
$n=Pn$
Thus, there are two ways to find the remainder when P(x) is divided by
$\left(x=n$ that is:
(1) use synthetic division, or
(2) calculate P(n.
Similarly, there are two ways to find the value $αx$
(1) substitute r in the polynomial expression P(X). or
(2) use synthetic division.
Example 1. Find the remainder when $\left(5x^{2}-2x.1\right)$ divided $y\left(x+2$
$0$ $0n$
a. Using the Remainder $m00m$
P(x) = $2-2x+1$ $==3$
= 5(-2) - 2(-2) + 1
PPP(((---222) ) ) = 5(4) + 4+1
= 20 +4 +1= 25
Therefore, the remainder when P(x) divided by x+
is 25.
b. Using synthetic division: $s2-2.1$
-2
Thus, the $m$ $4$ is 26.
$2$ Find the remainder when $\left(x\right)=2x^{4}+53+2^{2}-7x-15$
$a$ $a-4bx\left(2.-3\right)$
$so$ $aoa$
$n$ $mo0m$ $3$ $m$ $2$ $s$ $2\left(x--\right).tn$ $r=3$ $2$ $nn=2$ $+5$ $+2^{2}-7x-15$
$P\left(\dfrac {3} {2}\right)=2\left(\dfrac {3} {2}\right)^{4}.s\left(\dfrac {3} {2}\right)^{3}+2\left(\dfrac {3} {2}\right)^{2}-7\left(\dfrac {3} {2}\right)-15$
Thus, $P\left(\dfrac {3} {2}\right)=6$ $2x$ $5x.2x^{2-7x-16}-2^{2.s^{2.+4x.14.\dfrac {6} {\times -\dfrac {3} {2}}}}$ $3$ $x--$

10th-13th grade

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Solution

Qanda teacher - Askhina

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