In each of the following, divide the polynomial f(x) by g(x) and find the quotient and remainder.. f(x)= 6x^5+4x^4-3x^3+x+1 g(x)= 3x^2-x+1
Plz explain step by step
Answers
Step-by-step explanation:
this is the correct answer
Answer:
✡Quotient=2x³+2x²-x-1 and remainder=x+2☑
Step-by-step explanation:
3x²-x+1)6x^5+4x⁴-3x³+x+1(2x³+2x²-x-1
6x^5-2x⁴+2x³
- + -
_________________
6x⁴-5x³+x
6x⁴-2x³+2x²
- + -
_______________
-3x³-2x²+x
-3x²+x²-x
+ - +
____________
-3x²+2x+1
-3x²+x - 1
+ - +
____________
x+2
✅Hence,the quotient is 2x³+2x²-x-1 and remainder is x+2.
Proof⤵
➡Dividend=Divisor×Quotient+remainder
➡(3x²-x+1)(2x³+2x²-x-1) +x+2
➡3x²(2x³+2x²-x-1) -x(2x³+2x²-x-1) +1(2x³+2x²-x-1) +x+2
➡6x^5+6x⁴-3x³-3x²-2x⁴-2x³+x²+x+2x³+2x²-x-1+x+2
➡6x^5+6x⁴-2x⁴-3x³-2x³+2x³-3x²+x²+2x²+x-x+x-1+2
➡6x^5+4x⁴-3x³+x+1=LHS
RHS=LHS
Hence proofed
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