Math, asked by mayank8379, 11 months ago

using remainder theorem find the remainder when x cube + x square - 2 x minus 3 is divided by 2 X + 3​

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Answers

Answered by vatsal00
18

\huge\mathbb{A~N~S~W~E~R}

Let we,

p(x) = 2x + 3 \\  \\ p(0) = 2x + 3 \\  \\ 0 = 2x + 3 \\  \\  - 3 = 2x \\  \\  x =  \frac{ - 3}{2}

Use value of x in fiven polynomial.

 =  {x}^{3}  +  {x}^{2}  - 2x + 3 \\  \\  =  {( \frac{- 2}{3}) }^{3}  +  {( \frac{ - 2}{3} )}^{2}  - 2( \frac{ - 2}{3} ) + 3 \\  \\  =  \frac{ - 8}{27}  +  \frac{4}{9}  +  \frac{4}{3}  + 3 \\  \\  =  \frac{ - 8 + 12 + 36 + 81}{27}  \\  \\  =  \frac{121}{27}

{\huge\color{Red}{Answer~is~\frac{121}{27}~ .  }}

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Answered by erinna
5

The remainder is -9/8.

Step-by-step explanation:

The given polynomial is

f(x)=x^3+x^2-2x-3

Remainder theorem: If a polynomial is divided by P(x) is divided by (x-c), then remainder is P(c).

We need to find the remainder when the given polynomial is divide by (2x+3).

2x+3=0\Rightarrow x=-\dfrac{3}{2}

Using remainder theorem the remainder is f(-3/2).

Substitute x=-3/2 in the given function.

f(-\dfrac{3}{2})=(-\dfrac{3}{2})^3+(-\dfrac{3}{2})^2-2(-\dfrac{3}{2})-3

f(-\dfrac{3}{2})=-\dfrac{27}{8}+\dfrac{9}{4}+3-3

f(-\dfrac{3}{2})=\dfrac{-27+19}{8}

f(-\dfrac{3}{2})=-\dfrac{9}{8}

Therefore, the remainder is -9/8.

#Learn more

The polynomials p(x)=ax³+4x²+3x-4 and q(x)=x³-4x+a leaves the same remainder when divided by (x-3) find the remainder when p(x) is divided by (x-2).

https://brainly.in/question/1228617

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