+309 1. Cristoble used synthetic division to divide the polynomial f(x) by x + 3, as shown on the table.
What is the value of f(−3) ?
2.
Which binomial expressions are factors of 4x^3+9x^2−x−6?
Select EACH correct answer.
A) x−1
B) x + 2
C) x + 1
D) x−2
3.Three is a zero of the equation x^3−4x^2−3x+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)^2=0
D) (x+2)(x−√3)(x+√3)=0
4.
Which values are possible rational roots of 4x^3+9x^2−x+10=0 according to the rational root theorem?
Select EACH correct answer.
A) ±52
B) ±25
C) ±12
D) ±2
+128406 1) f(-3) = 36
2) 4x^3+9x^2−x−6
-1 is a root because 4(-1)^3 + 9(-1)^2 - (-1) - 6 = -4 + 9 + 1 - 6 = -5 + 5 = 0
So (x + 1) is one factor
Performing some synthetic division to find the remaining polynomial we have
-1 [ 4 9 - 1 - 6 ]
-4 -5 6
________________
4 5 -6
So....the remaining polynomial is 4x^2 + 5x - 6
Factoring this we have
( 4x - 3) ( x + 2)
So...the factors are ( x + 1) (x + 2) (4x - 3)
3) Since we know that 3 is a zero...we can perform some synthetic division to find the other factors
3 [ 1 - 4 - 3 18 ]
3 -3 -18
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1 -1 -6
The remaining polynomial is x^2 - x - 6 which factors as (x - 3) ( x + 2)
So...the factorization is
(x - 3) ( x - 3) ( x + 2) = (x + 2) (x - 3)^2
4) Possible rational roots = all the factors of 10 = 1, 2, 5, 10 over all the factors of 4 = 1, 2, 4
So... ±5/2 , ±1/2 and ± 2
