Question

Q1.find the remainder when x^3-6x^2+-9x+13 is divided by x+1

Answer 1

Explanation:

Given

We have given f(x)= x³-6x²-9x+13

To Find

We have to find the remainder and to divide the f(x) by x+1

$\sf\huge {\underline{\underline{{Solution}}}} </p><p>Solution$

How to solve ?

Step 1: Write down the both dividend and divisor firstly.

Step 2: Multiply the Divisor in accordance with degree of the dividend and it's Coefficient and continue the division process.

x³-6x²-9x+13

Now ,in order to make x³ Multiply the x+1 with x²

=> x²(x+1)= x³+x²

x³-6x²-9x+13

x³+x²

(-)(-)

_______

-7x²-9x+13

Now,in order to make -7x² Multiply the divisor with -7x => -7x( x+1)= -7x²-7x

-7x²-9x+13

-7x²-7x

(+)(+)

_______

-2x+13

Now, Multiply the Divisor with -2

=> -2(x+1)= -2x -2

-2x+13

-2x-2

(+)(+)

_______

15

______

Dividend = x³-6x²-9x+13

Divisor= x+1

Quotient= x²-7x-2

Remainder = 15

Now, check the above resulta by division algorithm:

Dividend= Divisor * quotient + Remainder

x³-6x²-9x+13= (x+1)*(x²-7x-2)+15

x³-6x²-9x+13=x³-7x²-2x+x²-7x-2+15

x³-6x²-9x+13= x³-6x²-9x+13