Question

find the quotient and remainder when 2x³+3x²-9x+4 is divided by 2x-1

Answer 1

Here's your answer

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Let p(x)=2x³+3x²-9x+4

Let q(x)=2x-1

Now, p(x)÷q(x)

By Remainder Theorem:

Remainder=p(1/2)

=2×(1/2)³+3(1/2)²-9(1/2)+4

=1/4+3/4-9/2+4

=(1+3-18+16)/4

=2/4

Remainder==> 1/2

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Hope it helps✌

Answer 2

$\huge \boxed{ \underline{ \underline{ \bf{Answer}}}}$

$\sf{p(x) = 2 {x}^{3} + 3 {x}^{2} - 9x + 4}$

$\sf{g(x) = 2x - 1}$

We have to find the quotient and remainder.

Now after dividing p(x) by g(x) we can get the values of each.

The process of division is in the attachment.

Therefore, after dividing we get,

$\boxed{ \sf{Quotient = {x}^{2} + 2x - \frac{7}{2}} }$

$\boxed{ \sf{Remainder = \frac{1}{2} }}$