Question

find the reminder when x³+3x²++1 divided by x-1/2​

Answer 1

GIVEN

p(x) = x^3 + 3x^2 +1

g(x) = x - 1/2

TO FIND :- Remainder when p(x) is divided by g(x)

SOULTION

As the degree of g(x) is 1 instead of long division method we can apply remainder theorem.

Remainder Theorem states that when we insert the zero of g(x) in place of x in p(x) then the result is equal to its remainder.

Now zero of g(x)

x - 1/2 = 0

=> x = 1/2

Hence the zero of g(x) = 1/2

We can put this value in p(x)

$p(x) = {x}^{3} + 3 {x}^{2} +1 \\ \\ \\ p( \frac{1}{2} ) = { (\frac{1}{2}) }^{3} + 3 {( \frac{1}{2} })^{2} + 1 \\ \\ \\ = \frac{1}{8} + \frac{3}{4} + 1 \\ \\ \\ = \frac{7}{8} + 1 \\ \\ \ \ = = \frac{15}{8} = 1 \frac{7}{8} (ans)$

Hence the remainder when p(x) divided by g(x) is 15/8 (ANS).

Answer 2

Step-by-step explanation:

x³ + 3x² + 1

divided by, ( x -1/2)

so x -1/2= 0

x =1/2

put the value of x (=1/2) in

x³ + 3x² + 1

now ( 1/2)³ + 3(1/2)² + 1

1/8 + 3/4 +1

1+6+8/8

15/8

reminder =15/8