If f(x)=x^3-9x^2+11x+21f(x)=x 3 −9x 2 +11x+21 and x-3x−3 is a factor of f(x)f(x), then find all of the zeros of f(x)f(x) algebra
ically.
1 answer:
Answer:
x = -1, 3, and 7
Step-by-step explanation:
Using grouping:
f(x) = x³ − 9x² + 11x + 21
f(x) = x³ − 9x² + 18x − 7x + 21
f(x) = x (x² − 9x + 18) − 7 (x − 3)
f(x) = x (x − 6) (x − 3) − 7 (x − 3)
f(x) = (x² − 6x) (x − 3) − 7 (x − 3)
f(x) = (x² − 6x − 7) (x − 3)
f(x) = (x + 1) (x − 7) (x − 3)
To use long division, see the picture.
The zeros are x = -1, 3, and 7.
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Answer:
Step-by-step explanation:
Given two points on the line (0, 16) and (3, 40), an equation for the line can be written using the slope-intercept line equation which takes the format .
Where,
b = y-intercept or the point at which the line cuts the y-axis.
Let's find slope (m) using the slope formula:
Let,
Find b. Substitute the values of x = 0, y = 16, and m = 8 in the slope-intercept formula to find b.
Plug in the values of m and b into the slope-intercept formula to get the equation of the line.
Let's use the equation to find x when y = 112.
Substitute y = 112 in the equation
Divide both sides by 8