Mathematics: Find the quotient and the remainder of (4x^3+10x^2+12x+1) / (2x^2+3x).

Find the quotient and the remainder of (4x^3+10x^2+12x+1)

richisolano14

05.01.2022

$4x^3=2x\cdot2x^2$ , and 2x(2x^2+3x)=4x^3+6x^2 . Subtract this from the numerator to get a remainder of

(4x^3+10x^2+12x+1)-(4x^3+6x^2)=4x^2+12x+1

$4x^2=2\cdot2x^2$ , and 2(2x^2+3x)=4x^2+6x . Subtract this from the previous remainder to get a new remainder of

(4x^2+12x+1)-(4x^2+6x)=6x+1

is not divisible by 2x^2 , so we're done, and we've found that

$\dfrac{4x^3+10x^2+12x+1}{2x^2+3x}=2x+\dfrac{4x^2+12x+1}{2x^2+3x}$

$\dfrac{4x^3+10x^2+12x+1}{2x^2+3x}=2x+2+\dfrac{6x+1}{2x^2+3x}$

so that the quotient is 2x+2 with remainder 6x+1 .

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24lbriscoe

11.08.2021

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