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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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Qanda teacher - Askhina
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