Which of the following represents the zeros of f(x) = x3 − 11x2 + 38x − 40?
1 answer:
The answer is <span>5, 4, 2
</span>
Among all choices we have 5, so
x = 5
x - 5 = 0
Let's divide the expression by (x - 5) using the long division:
x³ - 11x² + 38x - 40
(x - 5) * x² = x³ - 5x² Subtract
____________________________
-6x² + 38x - 40
(x - 5) * (-6x) = -6x² + 30x Subtract
____________________________
8x - 40
(x - 5) * 8 = 8x - 40 Sutract
____________________________
0
Thus: x³ - 11x² + 38x - 40 = (x - 5)(x² - 6x + 8)
Now, let's simplify x² - 6x + 8.
x² - 6x + 8 = x² - 2x - 4x + 8 =
= x² - 2*x - (4*x - 4*2) =
= x(x - 2) - 4(x - 2) =
= (x - 4)(x - 2)
Hence:
x³ - 11x² + 38x - 40 = (x - 5)(x - 4)(x - 2)
To calculate zero:
x³ - 11x² + 38x - 40 = 0
(x - 5)(x - 4)(x - 2) = 0
x - 5 = 0 or x - 4 = 0 or x - 2 = 0
x = 5 or x = 4 or x = 2
You might be interested in
Answer:
4 because 4 is the exponent
Step-by-step explanation:
$3.50
702/18= 39 (so you have 39 boxes of cookies)
$136.50/39= $3.50 (so each box cost 3.5)
3.5 x 39= 136.5
Answer:
11.5
Step-by-step explanation:
98.9 / 8.6 = 11.5
The slope of the perpendicular line of y=5x would be -1/5, since slopes are always opposite reciprocals when they are perpendicular to each other.
Answer: 117,649
Step-by-step explanation: