Question

answer this please
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Answer 1

Que : x3+3x2+3x+1 ÷ x-1/2

explanation ;

Answer ; x2-5/2x-1

Answer 2

Answer:  The required remainder is $\dfrac{27}{8}.$

Step-by-step explanation:  We are given to find the remainder when the following polynomial is divided by the linear factor $(x-\frac{1}{2}).$

$f(x)=x^3+3x^2+3x+1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Remainder Theorem :   When a polynomial p(x) is divided by the liner factor (x - a), then the remainder is p(a).

So, for the given polynomial (i), when divided by  $(x-\frac{1}{2}),$ the remainder will be given by

$f(\frac{1}{2})\\\\=\left(\dfrac{1}{2}\right)^3+3\times\left(\dfrac{1}{2}\right)^2+3\times\dfrac{1}{2}+1~~~~~~~~~~~~~~~~[\textup{Using expression for f(x) from (i)}]\\\\\\=\dfrac{1}{8}+\dfrac{3}{4}+\dfrac{3}{2}+1\\\\\\=\dfrac{1+6+12+8}{8}\\\\\\=\dfrac{27}{8}.$

Thus, the required remainder is $\dfrac{27}{8}.$