To find the zeros of f(x), we need to find the values of x for which f(x) equals zero.
Since x - 4 is a factor of f(x), we can set f(x) equal to zero and solve for x:
6x^3 - 31x^2 + 18x + 40 = 0
We can use synthetic division to find the remaining zeros of f(x).
Dividing by x - 4, we get:
4 | 6 -31 18 40
24 -28 -40
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30 -10 0
This tells us that x - 4 is a factor of f(x), and the reduced equation is:
6x^2 - 10x + 0 = 0
Factoring out an x, we have:
x(6x - 10) = 0
Setting each factor equal to zero, we get:
x = 0 or 6x - 10 = 0
For the second equation, solving for x gives:
6x = 10
x = 10/6 = 5/3
So, the zeros of f(x) are x = 0, x = 5/3, and x = 4.
If f, left bracket, x, right bracket, equals, 6, x, cubed, minus, 31, x, squared, plus, 18, x, plus, 40f(x)=6x
3
−31x
2
+18x+40 and x, minus, 4x−4 is a factor of f, left bracket, x, right bracketf(x), then find all of the zeros of f, left bracket, x, right bracketf(x) algebraically.
1 answer