find the remainder when x^3-6x^2+-9x+13 is divided by x+1
Answers
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
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
Step-by-step 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
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