Melinda and Marcus are saving money to purchase a present for a friend. Each friend starts with an amount and also saves a speci
fic amount each week.
Melinda created a table to show the total she has saved at the end of each week.
Weeks: 0 5 10 15 20 25 30 35 40
Amount: 75 135 195 255 315 375 435 495 555
Marcus came up with the following equation to show the total, y, he has saved at the end of each week, x.
y = 14x + 25
Compare the rate at which each friend saves money.
Select the correct answer from the drop-down menu to complete the statement.
The rate at which Melinda is adding to her savings each week is $
less than the rate at which Marcus is adding to his savings each week.
Melinda created a table to show the total she has saved at the end of each week.
Weeks: 0 5 10 15 20 25 30 35 40
Amount: 75 135 195 255 315 375 435 495 555
Marcus came up with the following equation to show the total, y, he has saved at the end of each week, x.
y = 14x + 25
Compare the rate at which each friend saves money.
Select the correct answer from the drop-down menu to complete the statement.
The rate at which Melinda is adding to her savings each week is $
less than the rate at which Marcus is adding to his savings each week.
2 answers:
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Answer:
YES
NO
NO
Step-by-step explanation:
The given polynomial is:
(x - a) is a factor of a polynomial iff x = a is a solution to the polynomial.
To check if (x - 5) is a factor of the polynomial f(x), we substitute x = 5 and check if it satisfies the equation.
∴ f(5) = 5³ + 4(5)² - 25(5) - 100
= 125 + 100 - 125 - 100
= 225 - 225
= 0
We see, x = 5 satisfies f(x). So, (x - 5) is a factor to the polynomial.
Now, to check (x + 2) is a factor.
i.e., to check x = - 2 satisfies f(x) or not.
f(-2) = (-2)³ + 4(-2)² - 25(-2) - 100
= -8 + 16 + 50 - 100
= -108 + 66
≠ 0
Therefore, (x + 2) is not a factor of f(x).
To check (x - 4) is a factor.
∴ f(4) = 4³ + 4(4)² - 25(4) - 100
= 64 + 64 - 100 - 100
= 128 - 200
≠ 0
Therefore, (x - 4) is not a factor of f(x).