Question

Divide x^3+2x^4+6x-9 by x^3+3​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer :-

• Quotient - (2x+1)

• Remainder - (-12)

Method For Dividing :-

$\tt \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:2x + 1 \\ \tt {x}^{3} + 3 \: \mid \overline{2 {x}^{4} + {x}^{3} + {x}^{2} + 6x - 9} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt \: \: 2 {x}^{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + 6x \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \: - \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - \: \: \: \: \: \: \: \: } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt \: \: \: \: \: \: \: {x}^{3} + {x}^{2} - 9 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt \: \: {x}^{3} \: \: \: \: \: \: \: \: \: \: \: + 3 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \underline{ - \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - \: \: \: \: \: \: } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \: \: \: \: \tt \: \: \: \: \: \: \: \: \: \: \: \: \: - 12 \: \: }$

So, after dividing we get that the quotient is 2x+1 and the remainder is -12

Verification :-

$\sf{\boxed{\red{\dfrac{Dividend}{Divisor}=quotient+\dfrac{Remainder}{Divisor}}}}$

As , we know the value of Dividend, Divisor , quotient and Remainder. Put those value in the formula for the verification of our answer.

L.H.S

$\sf{\boxed{\dfrac{2\ x^{4}+\ x^{3}+6x-9}{\ x^{3}+3}}}$

R.H.S

$\sf{(2x+1)+(\dfrac{-12}{\ x^{3}+3})}$

$\sf{(2x+1)-(\dfrac{12}{\ x^{3}+3})}$

• Now , take the LCM and solve the equation

$\sf{\dfrac{2\ x^{4}+\ x^{3}+6x+3-12}{\ x^{3}+3}}$

$\sf{\boxed{\dfrac{2\ x^{4}+\ x^{3}+6x-9}{\ x^{3}+3}}}$

Hence Verified !

$\sf{\underline{\underline{\orange{Some\:points\:related\:to\:Divide}}}}$

1. On dividing if there are same signs (+ , +) or (- , -) then the answer will be positive
2. If the signs are different (+ , -) then the answer will be negative