Learn polynomial long division with these two examples that are easy to follow and straight to the point.
Example #1
Divide x2 + 3x - 10 by x - 2
Divide the leading term of x2 + 3x - 10 by the leading term of x - 2
x2 ÷ x = x
Write x as the first term of the quotient
x
x - 2) x2 + 3x - 10
Multiply the first term 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
Bring down -10
x
x - 2) x2 + 3x - 10
-x2 + 2x
______________
5x - 10
Divide the leading term of 5x - 10 by the leading term of x - 2
5x ÷ x = 5
Write 5 as the second term of the quotient. Since 5 is positive, you can put a + sign between the first term and the second term.
x + 5
x - 2) x2 + 3x - 10
-x2 + 2x
______________
5x - 10
Multiply the second term 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
Example #2
Divide x2 - 5x + 1 by x + 3
Divide the leading term of x2 - 5x + 1 by the leading term of x + 3
x2 ÷ x = x
Write x as the first term of the quotient
x
x + 3) x2 - 5x + 1
Multiply the first term 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
Bring down 1
x
x + 3) x2 - 5x + 1
-x2 - 3x
______________
-8x + 1
Divide the leading term of -8x + 1 by the leading term of x + 3
-8x ÷ x = -8
Write -8 as the second term of the quotient. Notice that putting a + sign between the first term and the second term does not change the problem.
x + -8
x + 3) x2 - 5x + 1
-x2 - 3x
______________
-8x + 1
Multiply the second term 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 remainder of 25
May 26, 22 06:50 AM
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