If f(x)=x^3-4x^2-25x+28f(x)=x 3 −4x 2 −25x+28 and x-7x−7 is a factor of f(x)f(x), then find all of the zeros of f(x)f(x) algebra
ically.
1 answer:
9514 1404 393
Answer:
x = {7, 1, -4}
Step-by-step explanation:
Dividing the given factor from the polynomial using synthetic division, we get ...
f(x) = (x -7)(x^2 +3x -4)
Factoring the quadratic* gives ...
f(x) = (x -7)(x -1)(x +4)
The zeros are the values of x that make these factors be zero:
x = {7, 1, -4}
_____
* The constants in the binomial factors are factors of -4 that have a sum of +3. Those are (-1)(4) = -4. -1+4 = 3.
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Since these questions all require similar methods of solving, I will only completely work out the first question of each type.
2. To find
as a decimal, all we need to do is complete the fraction by dividing the numerator by the denominator.
= 7 / 10 = 0.7
as a decimal is 0.7.
3. To write a fraction as a percentage, we must first convert it into a decimal, the way we did in problem 2.
Then to change that number into a percentage, we can either multiply it by 100, or (my personal shortcut) just shift the decimal point over two places to the right.
0.65 = 65%
which is the answer to question 3.
written as a percent is 65%.
4. Writing a percentage as a fraction is a bit easier than writing a fraction as a percentage. All you need to do is place the percentage in the numerator's place of a fraction with 100 as the denominator and simplify.
2%5 =
Since 25 goes into 100 four times, we can simplify this fraction.
which is our answer.
25% written as a fraction is
.
5. This is the same as problem 3, so I won't show my work for the sake of time.
as a percentage is 40%.
6. This is the same as problem 1, so I will not show steps again.
as a decimal is 0.15.
7. Done similar problems in past. No work shown.
as a percent is 42%.
8. Same as last problem.
as a percent is 4%.
9. Same as number 4.
6% as a fraction is
.
10. Similar in past.
as a percentage is 60%.
11. Same as 6.
as a decimal is 0.48.
12. Done a lot of these so far.
as a percentage is 30%.
13. Just did one like this.
as a percentage is 75%.
14. Same as 4 and 9.
65% as a fraction is.
15. Plenty of these done in past.
as a percentage is 20%.
16. Last problem, and it's just like the one just before this.
written as a percent is 90%.
So there are the results.
Hope that helped! =)
2. To find
3. To write a fraction as a percentage, we must first convert it into a decimal, the way we did in problem 2.
Then to change that number into a percentage, we can either multiply it by 100, or (my personal shortcut) just shift the decimal point over two places to the right.
0.65 = 65%
which is the answer to question 3.
4. Writing a percentage as a fraction is a bit easier than writing a fraction as a percentage. All you need to do is place the percentage in the numerator's place of a fraction with 100 as the denominator and simplify.
2%5 =
Since 25 goes into 100 four times, we can simplify this fraction.
which is our answer.
25% written as a fraction is
5. This is the same as problem 3, so I won't show my work for the sake of time.
6. This is the same as problem 1, so I will not show steps again.
7. Done similar problems in past. No work shown.
8. Same as last problem.
9. Same as number 4.
6% as a fraction is
10. Similar in past.
11. Same as 6.
12. Done a lot of these so far.
13. Just did one like this.
14. Same as 4 and 9.
65% as a fraction is
15. Plenty of these done in past.
16. Last problem, and it's just like the one just before this.
So there are the results.
Hope that helped! =)