Answer:
- Trinomials that can be factored into two binomials are:
1. x² + 5x + 6
Factored to: (x + 3)(x + 2)
2. x² + x - 2
Factored to: (x - 1)(x + 2)
Example of a Trinomial that cannot be factored into two binomials:
x² + 5x + 1
Explanation:
- A trinomial is a polynomial that consist of three terms. It is in the form:
ax² + bx + c.
- A binomial is a polynomial that consists of two terms. It is of the form:
bx + c.
A trinomial is said to be factorable if the can be written as a product of two binomials.
Example 1:
The expression: x² + 5x + 6
Can be rewritten as:
x² + 2x + 3x + 6
Grouping this, we have
(x² + 2x) + (3x + 6)
Which becomes
x(x + 2) + 3(x + 2)
Factoring (x + 2), we have
(x + 3)(x + 2)
Which is a product of two binomials as required.
Therefore, the expression is factorable.
Example 2:
The trinomial expression:
x² + x - 2
Can be written as:
x² + 2x - x - 2
= (x² + 2x) - (x + 2)
= x(x + 2) - (x + 2)
Factoring (x + 2), we have
(x - 1)(x + 2)
This a product of two binomials, hence, the tutorial is factorable.
Example 3:
Consider the trinomial:
x² + 5x + 1
This is not factorable, because the term 5x cannot be split into a sum or difference, in such a way that it has a common factor with x² and with 1.
Unlike in the case of Example 1.
x² + 5x + 6
5x was split into the sum of 2x and 3x
That is, x² + 5x + 6 = x² + 2x + 3x + 6
So that, 2x has a common factor, x with x², and 3x has a common factor, 3 with 6.