Be taught polynomial lengthy division with two examples which might be straightforward to observe and straight to the purpose.

## Explaining in additional particulars the polynomial lengthy division within the determine above

The polynomial lengthy division above is a abstract displaying how one can do lengthy division with polynomials. Learn instance #1 to totally perceive it!

Instance #1

Divide x2 + 3x – 10 by x – 2

Divide the main time period of x2 + 3x – 10 by the main time period of x – 2

x2 ÷ x = x

Write x as the primary time period of the quotient

x
x – 2)  x2 + 3x – 10

Multiply the primary time period of the quotient by the divisor

x(x – 2) = x2 – 2x

Subtract x2 – 2x from the dividend

x
x – 2)  x2 + 3x – 10
-( x2 – 2x)

x
x – 2)  x2 + 3x – 10
-x2 + 2x
______________
5x

Carry down -10

x
x – 2)  x2 + 3x – 10
-x2 + 2x
______________
5x  – 10

Divide the main time period of 5x – 10 by the main time period of x – 2

5x ÷ x = 5

Write 5 because the second time period of the quotient. Since 5 is constructive, you’ll be able to put a + signal between the primary time period and the second time period.

x  +  5
x – 2)  x2 + 3x – 10
-x2 + 2x
______________
5x  – 10

Multiply the second time period of the quotient by the divisor

5(x – 2) = 5x – 10

Subtract 5x – 10 from 5x – 10

x  +  5
x – 2)  x2 + 3x – 10
-x2 + 2x
______________
5x  – 10
-5x + 10
__________
0

(x2 + 3x – 10) ÷ (x – 2) = x + 5

## One other easy instance displaying polynomial lengthy division

Instance #2

Divide x2 – 5x + 1 by x + 3

Divide the main time period of x2 – 5x + 1 by the main time period of x + 3

x2 ÷ x = x

Write x as the primary time period of the quotient

x
x + 3)  x2 – 5x + 1

Multiply the primary time period of the quotient by the divisor

x(x + 3) = x2 + 3x

Subtract x2 + 3x from the dividend

x
x + 3)  x2 – 5x + 1
-( x2 + 3x)

x
x + 3)  x2 – 5x + 1
-x2 – 3x
______________
-8x

Carry down 1

x
x + 3)  x2 – 5x + 1
-x2 – 3x
______________
-8x  + 1

Divide the main time period of -8x  + 1 by the main time period of x + 3

-8x ÷ x = -8

Write -8 because the second time period of the quotient. Discover that placing a + signal between the primary time period and the second time period doesn’t change the issue.

x + -8
x + 3)  x2 – 5x + 1
-x2 – 3x
______________
-8x  + 1

Multiply the second time period of the quotient by the divisor

-8(x + 3) = -8x – 24

Subtract -8x – 24 from -8x + 1

x  + -8
x + 3)  x2 – 5x + 1
-x2 – 3x
______________
-8x  + 1
8x + 24
__________
25

(x2 – 5x + 1) ÷ (x + 3) = x + -8 with a the rest of 25

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