Question

by long division , find the remainder when the polynomial 2x^4-3x^3+5x^2-4x-3 is divided by x-2 . ​

Answer 1

this is your answer dear have a good day

$ANSWER</p><p></p><p></p><p>The division algorithm states that Dividend=Divisor×Quotient+Remainder that is f(x)=g(x)⋅q(x)+r(x)</p><p></p><p></p><p>Here, it is given that the dividend is f(x)=2x4−5x3+x2+3x−2, the divisor is 2x2−5x+3 and the remainder is −2x+1, therefore, by applying division algorithm we have:</p><p></p><p></p><p>2x4−5x3+x2+3x−2=(2x2−5x+3)g(x)+(−2x+1)⇒2x4−5x3+x2+3x−2−(−2x+1)=(2x2−5x+3)g(x)⇒2x4−5x3+x2+3x−2+2x−1=(2x2−5x+3)g(x)⇒2x4−5x3+x2+5x−3=(2x2−5x+3)g(x)⇒g(x)=2x2−5x+32x4−5x3+x2+5x−3 </p><p></p><p></p><p>Let us now divide 2x4−5x3+x2+5x−3 by 2x2−5x+3 as shown in the above image:</p><p></p><p></p><p>From the division, we observe that the quotient is x2−1 and the remainder is 0.</p><p></p><p></p><p>Hence, the quotient q(x)=x2−1.</p><p></p><p>$

Answer 2

Answer:

Quotient : 2x^3-x^2-3x-2

Remainder: 7