Question

directions: factor each polynomial. check your answers by foil.

1. $x^2 + 5x + 6$
2. $a^2 + 11a + 30$
3. $w^2 + 4w + 4$
4. $y^2 + 9y + 8$
5. $y^2 - 6y + 8$
6. $x^2 - 11x + 28$
7. $p^2 - 14p + 40$
8. $x^2 + 3x - 70$
9. $m^2 + 5m - 6$
10. $b^2 - 15b + 56$
11. $a^2 + 11a + 18$
12. $x^2 - 14x - 51$

Explanation:

Let's solve problem 2: \(a^2 + 11a + 30\)

Step 1: Find two numbers

We need two numbers that multiply to \(30\) (the constant term) and add up to \(11\) (the coefficient of the middle term). The numbers \(5\) and \(6\) work because \(5\times6 = 30\) and \(5 + 6 = 11\).

Step 2: Factor the polynomial

Using these two numbers, we can factor the quadratic polynomial as \((a + 5)(a + 6)\). We can check this using the FOIL method: \((a + 5)(a + 6)=a\times a + a\times6 + 5\times a + 5\times6 = a^2 + 6a + 5a + 30 = a^2 + 11a + 30\), which matches the original polynomial.

Answer:

\((a + 5)(a + 6)\)