Question

Using remainder theorem find the remainder when 7x³+40x²+22x-35is divided by( x+1)?

Answer 1

remainder = `-24`

Explanation:

Given: `(7x^3 + 40x^2 + 22x - 35)/(x+1)`

The Remainder Theorem states that when you divide a polynomial `f(x)` by a linear factor `(x-a)`, you will have a quotient function `q(x)` and a remainder.

The remainder `= f(a)`. This remainder can be found using long division, synthetic division or the Remainder Theorem.

Long Division:
`" "ul(" "7x^2 + 33x - 11)larr` quotient function
`x + 1| 7x^3 + 40x^2 + 22x - 35`
`" "ul(7x^3 + 7x^2)`
`" "33x^2 + 22x`
`" "ul(33x^2 + 33x)`
`" "-11x - 35`
`" "ul(-11x - 11)`
`" "-24 larr`remainder

Remainder Theorem:

linear factor: `(x-a) = (x +1) = (x - -1)`.

This means `a = -1`

`f(x) = 7x^3 + 40x^2 + 22x - 35`

`f(-1) = 7(-1)^3 + 40(-1)^2 + 22(-1) - 35 = -24`

Remainder `= -24`