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We will find the rational zeros of <span>f(x) = 3x^3 -5x^2 - 12x + 20
1) Arrange in descending order: </span><span>f(x) = 3x^3 -5x^2 - 12x + 20
2) write down the factors of the constant term, 20.
1,2, 4, 5, 10, 20 - these could all be the possible values of p.
3) write down the factors of the leading coefficient, 3.
1,3 - these are the possible values of q.
.
4) write down all the possible values of p/q. both positive and negative values must be written down. Simplify
1/1 ; 1/3 ; 2/1 ; 2/3 ; 4/1 ; 4/3 ; 5/1 ; 5/3 ; 10/1 ; 10/3 ; 20/1 ; 20/3
1 ; 0.33 ; 2 ; 0.67 ; 4 ; 1.33 ; 5 ; 1.67 ; 10 ; 3.33 ; 20 ; 6.67
5) use the simplified p/q in both positive and negative values in the synthetic division. Pls. see attachment for my synthetic division.
Based on my computations, </span>a factor of the polynomial f(x) = 3x^3 -5x^2 - 12x + 20 is: x = -1.67 or x = -5/3
IF THESE ARE THE MISSING CHOICES:
<span>A)2x + 1 B)2x - 1 C)3x+5 D)3x - 5.
</span>
MY ANSWER IS: D) 3x - 5.
1) Arrange in descending order: </span><span>f(x) = 3x^3 -5x^2 - 12x + 20
2) write down the factors of the constant term, 20.
1,2, 4, 5, 10, 20 - these could all be the possible values of p.
3) write down the factors of the leading coefficient, 3.
1,3 - these are the possible values of q.
.
4) write down all the possible values of p/q. both positive and negative values must be written down. Simplify
1/1 ; 1/3 ; 2/1 ; 2/3 ; 4/1 ; 4/3 ; 5/1 ; 5/3 ; 10/1 ; 10/3 ; 20/1 ; 20/3
1 ; 0.33 ; 2 ; 0.67 ; 4 ; 1.33 ; 5 ; 1.67 ; 10 ; 3.33 ; 20 ; 6.67
5) use the simplified p/q in both positive and negative values in the synthetic division. Pls. see attachment for my synthetic division.
Based on my computations, </span>a factor of the polynomial f(x) = 3x^3 -5x^2 - 12x + 20 is: x = -1.67 or x = -5/3
IF THESE ARE THE MISSING CHOICES:
<span>A)2x + 1 B)2x - 1 C)3x+5 D)3x - 5.
</span>
MY ANSWER IS: D) 3x - 5.