1. Kristina used synthetic division to divide the polynomial f(x) by x−2, as shown on the table.
What is the value of f(2)?
A).-14 B).-1 C).-2 D).-1
2. Which binomial expressions are factors of 2x3+5x2−x−6?
Select each correct answer.
X+1
X-2
X-1
X+2
3. Three is a zero of the equation x3−4x2−3x+18=0.
Which factored form is equivalent to the equation?
A). (x−2)(x−3)(x+3)=0
B). (x+2)(x−3)2=0
C). (x+2)(x−3√)(x+3√)=0
D). (x−2)(x−3)2=0
+129930 The answer to the first one sould be -11
2x^3 +5x^2−x−6
Write 5x^2 as 4x^2 + x^2......and we have.....
2x^3 + 4x^2 + x^2 - x - 6
2x^2 ( x + 2) + ( x + 2)(x - 3)
(x + 2) [ 2x^2 + x - 3]
(x + 2) (2x +3) (x - 1)
x^3−4x^2−3x+18 = 0
Using some synthetic division, we have
3 [ 1 - 4 -3 18 ]
3 -3 -18
_______________
1 -1 -6 0
The remaining polynomial is x^2 - x - 6 which factors as (x - 3) ( x + 2)
So .... the factored form is (x - 3) ( x - 3) ( x + 2) = ( x + 2) ( x - 3)^2 = 0
