Question

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

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Answer 1

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

✍akashbindjnvg✍

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