We want to make x^2-3x into a perfect square trinomial. An example of such a trinomial is x^2 + 6x + 9, which is equivalent to the square of (x+3).
From x^2-3x we see that the coefficient of x is -3. Divide this coefficient, -3, by 2, obtaining -3/2. Now square this result: square -3/2. Result: 9/4.
Adding 9/4 to x^2-3x makes x^2-3x into a perfect square trinomial.
<span>The fundamental idea of
multiplying is <em>repeated addition</em>. For example:
By taking the number five and add it itself three times we have:
In contrast, let's take the number
three and add it itself five times, so:
.
Both 3 and 5 are called
factors that are numbers. We can multiply them to get another number. Multiplying can also be expressed like this:
So you have the factors:
You can even write any multiplication as the
product of factors. On the other hands, factoring shows that you can write any nth-degree polynomial as the product of linear factors, so:
To conclude the <em>relationship</em> between both concepts is the
product of factors.</span>
Given data: Coach clausing had 4 teams with 5 players, 7 players and 8 players.
Total Number of players = 5 + 7 + 8
= 20
Number of teams = 4
Number of players in each team
= Total number of players ÷ Number of teams
= 20 ÷ 4
= 5
Hence, each team had 5 players.