Question

additional exercises 5.4
form ii
factoring trinomials
factor each polynomial completely, or state that the polynomial is prime.

1. ( x^2 - x - 30 )
2. ( x^2 - 13x + 42 )
3. ( y^2 + 15y + 36 )
4. ( y^2 - y - 90 )
5. ( a^2 + 10a + 16 )

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(16\) (the constant term) and add up to \(10\) (the coefficient of the middle term). The numbers are \(2\) and \(8\) since \(2\times8 = 16\) and \(2 + 8=10\).

Step2: Factor the trinomial

Using the numbers found, we can factor the trinomial \(a^{2}+10a + 16\) as \((a + 2)(a + 8)\) because when we expand \((a + 2)(a + 8)\) using the distributive property (FOIL method), we get \(a^{2}+8a+2a + 16=a^{2}+10a + 16\).

Answer:

\((a + 2)(a + 8)\)