(2u^3-13u^2-8u+7) divided by (u-7)
Start with this:
____________________
u - 7)2u³ - 13u² - 8u + 7
u on the far left divided into 2u³ gives 2u², so put 2u² on top of the line
2u² `
u - 7)2u³ - 13u² - 8u + 7
Multiply the 2u² by the u, getting 2u³, write that down under the
other 2u²:
2u² `
u - 7)2u³ - 13u² - 8u + 7
2u³
Multiply the 2u² by the -7, getting -14u², write that down under the
-13u²:
2u² `
u - 7)2u³ - 13u² - 8u + 7
2u³ - 14u²
Draw a line at the bottom:
2u² `
u - 7)2u³ - 13u² - 8u + 7
2u³ - 14u²
Now we subtract, by thinking of changing the sign of
the 2u³ to -2u³ and adding, and so it cancels out.
We also subtract the other terms, by thinking of changing
the sign of the -14u² to +14u² and adding, and we get +1u²
or just u². We write that below the line:
2u² `
u - 7)2u³ - 13u² - 8u + 7
2u³ - 14u²
u²
Now we bring down the -8u:
2u² `
u - 7)2u³ - 13u² - 8u + 7
2u³ - 14u²
u² - 8u
u on the far left divided into u² at the bottom, gives + u,
so put + u on top of the top line
2u² + u `
u - 7)2u³ - 13u² - 8u + 7
2u³ - 14u²
u² - 8u
Multiply the u on top by the u at the far left, getting u²,
write that down under the other u²:
2u² + u `
u - 7)2u³ - 13u² - 8u + 7
2u³ - 14u²
u² - 8u
u²
Multiply the u on top by the - 7, getting -7u, write that
down under the 8u:
2u² + u `
u - 7)2u³ - 13u² - 8u + 7
2u³ - 14u²
u² - 8u
u² - 7u
Draw a line at the bottom:
2u² + u `
u - 7)2u³ - 13u² - 8u + 7
2u³ - 14u²
u² - 8u
u² - 7u
Now we subtract, by thinking of changing the sign of
the lower u² to -u³ and adding, and so it cancels out.
We also subtract the other terms, by thinking of changing
the sign of the - 8u to +8u and adding, and we get -u.
We write that below the line:
2u² + u `
u - 7)2u³ - 13u² - 8u + 7
2u³ - 14u²
u² - 8u
u² - 7u
-u
Now we bring down the + 7
2u² + u `
u - 7)2u³ - 13u² - 8u + 7
2u³ - 14u²
u² - 8u
u² - 7u
-u + 7
u on the far left divided into -u at the bottom, gives - 1,
so put - 1 on top of the top line
2u² + u - 1
u - 7)2u³ - 13u² - 8u + 7
2u³ - 14u²
u² - 8u
u² - 7u
-u + 7
Multiply the - 1 on top by the u at the far left, getting -u,
write that down under the other -u:
2u² + u - 1
u - 7)2u³ - 13u² - 8u + 7
2u³ - 14u²
u² - 8u
u² - 7u
-u + 7
-u
Multiply the - 1 on top by the - 7, getting + 7, write that
down under the other + 7
2u² + u - 1
u - 7)2u³ - 13u² - 8u + 7
2u³ - 14u²
u² - 8u
u² - 7u
-u + 7
-u + 7
Draw a line underneath:
2u² + u - 1
u - 7)2u³ - 13u² - 8u + 7
2u³ - 14u²
u² - 8u
u² - 7u
-u + 7
-u + 7
Now we subtract, by thinking of changing the sign of
the lower -u to +u and adding, and so it cancels out.
We also subtract the other terms, by thinking of changing
the sign of the + 7 to - 7 and adding, and we get 0.
We write that below the line:
2u² + u - 1
u - 7)2u³ - 13u² - 8u + 7
2u³ - 14u²
u² - 8u
u² - 7u
-u + 7
-u + 7
0
The remainder is 0. So we are done and the quotient is
u² + u - 1
When the remainder isn't 0 we have to add a fraction
expression to the quotient whose numerator is the remainder and whose
denominator is the divisor.
Edwin
