An 8th-degree polynomial needs 9 terms that involve
x⁸, x⁷, ..., x¹, and x⁰.
x=10 implies that (x-10) is a factor of the polynomial according to the Remainder theorem.
Let the polynomial be of the form
f(x) = a₁x⁸ + a₂x⁷ + a₃x⁶ +a₄x⁵ + a₅x⁴ + a₆x³ + a₇x² + a₈x + a₉
The first few lines of the synthetic division are
10 | a₁ a₂ a₃ a₄ a₅ a₆ a₇ a₈ a₉ ( the first row has 9 coefficients)
-----------------------------------------
a₁
Answer:
The first row has 9 coefficients.
Answer:
Step-by-step explanation:
<u>Expand the expression with the help of distributive property.</u>
- 2(q + 3)
- => (2 x q) + (2 x 3)
- => 2q + 6
Hence, the expanded expression is 2q + 6.
Answer:
a. ![$ \frac{\textbf{17}}{\textbf{4}} $](https://tex.z-dn.net/?f=%24%20%5Cfrac%7B%5Ctextbf%7B17%7D%7D%7B%5Ctextbf%7B4%7D%7D%20%24)
b. ![$ \frac{\textbf{3}}{\textbf{8}} $](https://tex.z-dn.net/?f=%24%20%5Cfrac%7B%5Ctextbf%7B3%7D%7D%7B%5Ctextbf%7B8%7D%7D%20%24)
Step-by-step explanation:
a. ![$ \textbf{3} \hspace{1mm} \textbf{+} \hspace{1mm} \textbf{1}\frac{\textbf{1}}{\textbf{4}} $](https://tex.z-dn.net/?f=%24%20%5Ctextbf%7B3%7D%20%5Chspace%7B1mm%7D%20%5Ctextbf%7B%2B%7D%20%5Chspace%7B1mm%7D%20%5Ctextbf%7B1%7D%5Cfrac%7B%5Ctextbf%7B1%7D%7D%7B%5Ctextbf%7B4%7D%7D%20%24)
A mixed fraction of the form ![$ a\frac{x}{y} = a + \frac{x}{y} $](https://tex.z-dn.net/?f=%24%20a%5Cfrac%7Bx%7D%7By%7D%20%3D%20a%20%2B%20%5Cfrac%7Bx%7D%7By%7D%20%24)
![$ \therefore 3 + 1\frac{1}{4} = 3 + 1 + \frac{1}{4} $](https://tex.z-dn.net/?f=%24%20%5Ctherefore%203%20%2B%201%5Cfrac%7B1%7D%7B4%7D%20%3D%203%20%2B%201%20%2B%20%5Cfrac%7B1%7D%7B4%7D%20%24)
![$ = 4 + \frac{1}{4} $](https://tex.z-dn.net/?f=%24%20%3D%204%20%2B%20%5Cfrac%7B1%7D%7B4%7D%20%24)
![$ = \frac{\textbf{17}}{\textbf{4}} $](https://tex.z-dn.net/?f=%24%20%3D%20%5Cfrac%7B%5Ctextbf%7B17%7D%7D%7B%5Ctextbf%7B4%7D%7D%20%24)
b. ![$ \textbf{2} \hspace{1mm} \textbf{-} \hspace{1mm} \textbf{1}\frac{\textbf{5}}{\textbf{8}} $](https://tex.z-dn.net/?f=%24%20%5Ctextbf%7B2%7D%20%5Chspace%7B1mm%7D%20%5Ctextbf%7B-%7D%20%5Chspace%7B1mm%7D%20%5Ctextbf%7B1%7D%5Cfrac%7B%5Ctextbf%7B5%7D%7D%7B%5Ctextbf%7B8%7D%7D%20%24)
A mixed fraction of the form ![$ -c\frac{a}{b} = - c - \frac{a}{b} $](https://tex.z-dn.net/?f=%24%20-c%5Cfrac%7Ba%7D%7Bb%7D%20%3D%20-%20c%20-%20%5Cfrac%7Ba%7D%7Bb%7D%20%24)
![$ \therefore 2 - 1\frac{5}{8} = 2 - 1 - \frac{5}{8} $](https://tex.z-dn.net/?f=%24%20%5Ctherefore%202%20-%201%5Cfrac%7B5%7D%7B8%7D%20%3D%202%20-%201%20-%20%5Cfrac%7B5%7D%7B8%7D%20%24)
![$ = 1 - \frac{5}{8} $](https://tex.z-dn.net/?f=%24%20%3D%201%20-%20%5Cfrac%7B5%7D%7B8%7D%20%24)
![$ = \frac{8 - 5}{8} $](https://tex.z-dn.net/?f=%24%20%3D%20%5Cfrac%7B8%20-%205%7D%7B8%7D%20%24)
![$ = \frac{\textbf{3}}{\textbf{8}} $](https://tex.z-dn.net/?f=%24%20%3D%20%5Cfrac%7B%5Ctextbf%7B3%7D%7D%7B%5Ctextbf%7B8%7D%7D%20%24)
Hence, the answer.
1 hour = 60 minutes
1 hour:45 minutes
= 60 minutes:45 minutes
=12 minutes:9 minutes