(x4-x3+2)÷(x+2) polynomial
Long division
synthetic division
reminder theorem
factor theorem
(Solution)
Answers
Given :-
x + 2 as a factor of Polynomial.
x+2)x⁴-x³+2(x³-3x²
x⁴ + 2x³
__________________
-3x³+2
-3x³ - 6x²
_________________
-6x²+2
Hence,
Remainder= -6x²+2
Step-by-step explanation:
Given:
To find: Solution of the division by
1) Long division
2) Synthetic division
3) Reminder theorem
4) Factor theorem
Solution:
1) Long Division:
Write both divisor and dividend polynomial ,perform division as division of decimals but here every time try to cancel the first term only .
As shown below
Quotient polynomial is
Remainder is 26
2) Synthetic division:
Write the coefficients of dividend in RHS and write the value of x from divisor in LHS.
Take 1 coefficients down,
Multiply it with -2 and place the value under coefficient of x³,add both and place down,repeat the process till end.
Quotient polynomial is
Remainder is 26
3) Remainder Theorem:
It states that if (x-a) is divisor of polynomial p(x) than p(a) is remainder.
On putting x=-2 in the polynomial the remainder can be calculated.
put x=-2
On division, Remainder is 26.
4) Factor theorem: It states that if (x-a) is a factor of polynomial p(x) than p(a)=0.
Put value of x from factor
in polynomial
Thus, x+2 is not a factor of polynomial.
Final answer:
Quotient of division is
Remainder is 26.
x+2 is not a factor of
Hope it will help you.
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