Pre calc - quiz 2

The Remainder Theorem

If you take a function f(x) and divide it by a binomial, f(x)/x-a the remainder is f(a)

What does f(a) represent in a polynomial function?

f(a) represents plugging in the value of x into the equation

If f(x) = 2x^3 -5x^2 + 6x - 12 and f(4) what does the new function look like

f(4) = 2(4)^3 - 5(4)^2 +6(4) -12

find f(4) from f(x) = 2x^3 -5x^2 + 6x - 12

f(4) = 2(4)^3 - 5(4)^2 +6(4) -12

f(4) = 2(64) - 5(16) +24 -12

f(4) = 128 - 80 +12

f(4) = 60

Use synthetic division to solve f(4) from f(x) = 2x^3 -5x^2 + 6x - 12

f(x) = 2x^3 -5x^2 + 6x - 12

4| 2, -5, 6, 12
|___8__12_72
2 3 18 60

if given a function like f(x) = 2x^4 - 3x^2 + 30, f(3) what would the synthetic division look like

3 | 2, 0, -3, 0, 30

The factor theorem

(For a polynomial f(x) if) fa=0 (x-a) is a factor

Divide polynomial by linear factor (method 1 long)

Algebraic long division

Divide polynomial by linear factor (method 2 I like)

Grid method

Formula for dividing polynomial

f(x)=q(x)d(x)+r(x)

(x-6)(x+3)

x^2 - 3x - 18

(x + 2)(x + 3)

(x - 3)(x - 4)

(x + 8)(x - 2)

x^2 + 5x + 6

x^2 -7x + 12

x^2 + 6x -16

5(3x + 4)(2x - 1)

30x² + 25x - 20

(7x - 2)(3x + 5)

21x² + 29x - 10