By remainder theorem, find the remainder when p(x) is divided by g(x) (iii) p(x) = x3 – 12x2 + 14x -3, g(x)= 2x – 1 – 1
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Answered by
0
Answer:
The Remainder Theorem states that when you divide a polynomial p(x) by any factor (x−a); which is not necessarily a factor of the polynomial; you will obtain a new smaller polynomial and a remainder, and this remainder is the value of p(x) at x=a, that is p(a).
Here, it is given that the polynomial p(x)=4x
3
−12x
2
+14x−3 and the factor is g(x)=2x−1, therefore, by remainder theorem, the remainder is p(
2
1
) that is:
p(
2
1
)=4(
2
1
)
3
−12(
2
1
)
2
+(14×
2
1
)−3=(4×
8
1
)−(12×
4
1
)+7−3
=
2
1
−3+7−3=
2
1
+1=
2
3
Hence, the remainder is r(x)=p(
2
1
)=
2
3
.
Step-by-step explanation:
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Answered by
1
Answer:
reminder will be -12.
full explanation is in the given picture.
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