Question
Using synthetic division, determine whether the numbers are zeros of the polynomial functions.
Using synthetic division, determine whether the numbers are zeros of the polynomial functions.
-5, -2 ; f(x) = 3x^3 + 10x^2 - 19x + 30
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Koala Tutor
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To determine if -5 and -2 are zeros of the polynomial, we will use synthetic division.
For -5:
3x^3 + 10x^2 - 19x + 30 = 0
3(-5)^3 + 10(-5)^2 - 19(-5) + 30 = 0
-375 + 250 + 95 + 30 = 0
-375 + 250 + 95 + 30 = 0
0 = 0
Since the result is 0, -5 is a zero of the polynomial function f(x).
For -2:
3x^3 + 10x^2 - 19x + 30 = 0
3(-2)^3 + 10(-2)^2 - 19(-2) + 30 = 0
-24 + 40 + 38 + 30 = 0
-24 + 40 + 38 + 30 = 0
0 = 0
Since the result is 0, -2 is also a zero of the polynomial function f(x).
Therefore, both -5 and -2 are zeros of the polynomial function f(x) = 3x^3 + 10x^2 - 19x + 30.
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