Question

aDivide the following polynomial using synthetic division, then place the answer in the proper location on the grid. Write answer in descending powers of x.

(x^3 - 7x^2 + 8 ) ÷ (x + 1)

Answer 1

help

Answer 2

help please

Answer 3

Let f(x) = x^3-7x^2+7x+15
By inspection (ie: guessing): f(-1) = -1 - 7 - 7 + 15 =0

By the factor theorem is f(-1) = 0 then (x+1) is a factor of f(x).

x^3-7x^2+7x+15 = (x+1)(Ax^2+Bx+C) where A, B and C are constants to be found either by long division or by comparing coefficients. I will be doing the latter as it's easier to show.

Coefficients of x^3: 1 = A

Coefficients of x^0 (constant term): 15 = C

Coefficients of x^2: -7 = A + B , B = -8

Thus f(x) = (x+1)(x^2-8x+15)

We need to now see if that quadratic factors and it will if the discriminant is a complete square: b^2-4ac = 8^2 - 4*1*15 = 64-60 = 4 so this does factor:

and so the factored expression is f(x) = (x+1)(x-3)(x-5)

Answer 4

i hope that helps u @gary4

Answer 5

here is your set up for synthetic division