divide 4t³-st²+7 by( t-1)
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Step-by-step explanation:
by Remainder theorem: If a polynomial P(x) is divided by (x-c), then the remainder is equal to P(c).
The given polynomial are
p(t)=4t3−st2+7
q(t)=t2+st+8
Using remainder theorem the remainder of p(t)t−1is p(1) and the remainder ofq(t)t−1 is q(1).
Substitute t=1 in the given functions.
p(1)=4(1)3−s(1)2+7⇒4−s+7=11−s
q(1)=(1)2+s(1)+8=1+s+8=9+s
It is given that if p(t) and q(t) divided by (t-1), then the remainder is same.
p(1)=q(1)
Substitute these values.
11-s=9+s
Add s on both sides.
11=9+s+s
11=9+2s
Subtract 9 from both sides.
11-9=2s
2=2s
Divide both sides by 2.
1=s
Therefore, the value of s is 1.
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