Divide the polynomial p (x) by the polynomial g (x) and find the quotient and remainder.
p(x) = 10x4+17x3
-62x2 + 30x - 3 , g(x )= 2x2+ 7x+ 1
Answers
Step-by-step explanation:
Given :-
p(x) = 10x⁴+17x³-62x²+ 30x - 3 ,
g(x )= 2x²+ 7x+ 1
To find :-
Divide the polynomial p (x) by the polynomial g (x) and find the quotient and remainder?
Solution :-
Given Polynomials are :
p(x) = 10x⁴+17x³-62x²+ 30x - 3 ,
g(x )= 2x²+ 7x+ 1
On dividing p(x) by g(x)
=> p(x) ÷ g(x)
2x²+7x+1)10x⁴+17x³-62x²+30x-3(5x²-9x-2
10x⁴+35x³+5x²
(-) (-) (-)
____________________
0 -18x³-67x² +30x
-18x³-63x² - 9x
(+) (+) (+)
______________________
0 - 4x² +39x - 3
- 4x² -14x -2
(+) (+) (+)
________________________
53x -1
________________________
Answer:-
Quotient for the given problem = 5x²-9x-2
Remainder for the given problem = 53x-1
Check:-
We know that
Division Rule :
Dividend = Divisor × Quotient + Remainder
=> (5x²-9x-2)×(2x²+ 7x+ 1)+(53x-1)
=> 5x²(2x²+ 7x+ 1)-9x(2x²+ 7x+ 1)-2(2x²+ 7x+ 1) +53x-1
=> 10x⁴+35x³+5x²-18x³-63x²-9x-4x²-14x-2+53x-1
=> 10x⁴+(35x³-18x³)+(5x²-63x²-4x²)+(-9x-14x+53x) -(1+2)
=> 10x⁴+17x³-62x²+30x-3
=> p(x)
Verified the given relation in the given problem.
Used formulae :-
Division Rule :
Dividend = Divisor × Quotient + Remainder