Divide using synthetic division: `(x^4-3x^3-15x^2+19x+30)` `-:` `(x-5)`
1 Answer
lemjay | High School Teacher | (Level 3) Senior Educator
`(x^4 - 3x^3 - 15x^2 + 19x + 30 ) -: (x-5)`
Using synthetic division, we would have the coefficients of x^4-3x^3-15x^2+19x+30 as our dividend and the root of x-5 as the divisor.
`5` `|` `1` `-3` `-15` `19` `30`
`---------------`
`1` Bring down 1. Then multiply 1 and 5.
Write the product at the bottom of -3.
`5` `|` `1` `-3` `-15` `19` `30`
`5` Add -3 and 5.
`---------------` Then, multiply the sum with 5.
`1 ` `2 ` Write the product below -15.
`5` `|` `1` `-3` `-15` `19` `30`
`5` `10` Add -15 and 10.
`---------------` Then, multiply the sum with 5.
`1` `2` `5` Write the product below 19.
`5` `|` `1` `-3` `-15` `19` `30`
`5` `10` `-25` Add 19 and 25.
`---------------` Then, multiply the sum with 5.
`1` `2` -`5` `-6` Write the product below 30.
`5` `|` `1` `-3` ` -15` `19` `30`
`5` `10` `-25` `-30 ` Add -30 and -30.
`----------------`
`1` `2` `-5` `-6` `0` These are the coefficients of the
quotient, with a degree of 3.
Hence, `(x^4-3x^3-15x^2+19x+30) -: (x-5) = x^3+2x^2-5x-6` .