Question 478857
My question is When a polynomial P(x) is divided by 2x+1, the quotient is {{{x^2-x+4}}} and the remainder is 3

<pre>
{{{"P(x)"/(2x+1) =(x^2-x+4) + 3/(2x+1)}}}

Multiply through by (2x+1)

{{{"P(x)"=(2x+1)(x^2-x+4) + 3}}}

{{{"P(x)"=2x^3-2x^2+8x+x^2-x+4 + 3}}}

{{{"P(x)"=2x^3-x^2+7x+7}}}

Checking:

      <u>       x² -  x + 4</u> 
2x + 1)2x³ - x² + 7x + 7
       <u>2x³ + x²</u>
           -2x² + 7x
           <u>-2x² -  x</u>
                  8x + 7
                  <u>8x + 4</u>
                       3

Edwin</pre>