Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.

Match the trinomials with their factors.

Trinomials:
1. [tex]a^2 - 12a + 20[/tex]
2. [tex]a^2 - 19a - 20[/tex]

Factors:
A. [tex](a - 10)(a - 2)[/tex]
B. [tex](a - 4)(a + 5)[/tex]
C. [tex](a - 10)(a + 2)[/tex]

Note: The following trinomial and factor pairs are not included as they do not form a correct match:
- [tex]z^2 + c - 20[/tex]
- [tex]e^2 - 9 + 2a + 20[/tex]



Answer :

Let's solve for the correct pairs of trinomials and their factors. We need to match the given trinomials with the correct factors.

Here are the given trinomials:
1. [tex]\( a^2 - 12a + 20 \)[/tex]
2. [tex]\( a^2 - 19a - 20 \)[/tex]

And here are the possible factors:
1. [tex]\( (a-2)(a-10) \)[/tex]
2. [tex]\( (a-4)(a+5) \)[/tex]
3. [tex]\( (a-20)(a+1) \)[/tex]

Matching Trinomials with Factors:

1. For the trinomial [tex]\( a^2 - 12a + 20 \)[/tex]:

To factorize this trinomial, we look for two numbers that multiply to give the constant term (20) and add to give the coefficient of the middle term (-12).

We find that [tex]\( (a - 2)(a - 10) \)[/tex] works since:
- [tex]\( (a - 2) \times (a - 10) = a^2 - 10a - 2a + 20 = a^2 - 12a + 20 \)[/tex]

Thus, [tex]\( a^2 - 12a + 20 \)[/tex] factors as [tex]\( (a - 2)(a - 10) \)[/tex].

2. For the trinomial [tex]\( a^2 - 19a - 20 \)[/tex]:

To factorize this trinomial, we look for two numbers that multiply to give the constant term (-20) and add to give the coefficient of the middle term (-19).

We find that [tex]\( (a - 20)(a + 1) \)[/tex] works since:
- [tex]\( (a - 20) \times (a + 1) = a^2 + a - 20a - 20 = a^2 - 19a - 20 \)[/tex]

Thus, [tex]\( a^2 - 19a - 20 \)[/tex] factors as [tex]\( (a - 20)(a + 1) \)[/tex].

Therefore, the correct pairs are:

[tex]\[ \begin{array}{ccc} \text{Trinomial} & & \text{Factor} \\ \hline a^2 - 12a + 20 & \longrightarrow & (a-2)(a-10) \\ a^2 - 19a - 20 & \longrightarrow & (a-20)(a+1) \\ \end{array} \][/tex]