Question

1. $c^2 - 26c - 56$
2. $y^2 - 5y - 84$
3. $x^2 - 11x + 24$
4. $x^2 - 14x + 49$
5. $y^2 - 17y + 72$
6. $m^2 - 15m + 50$
7. $g^2 - 16g + 48$
8. $c^2 - 3c + 2$
9. $x^2 + 13xy + 42y^2$
10. $a^2 - 4ab - $
11. $m^2 + 2mn - 24n^2$
12. $x^2 + 8xy - 20y^2$

multi - step factoring. look for a gcf first, then factor the trinomial.

1. $4n^2 + 12n + 8$
2. $2x^2 - 8x - 24$
3. $3y^2 - 15y + 12$
4. $3a^3 + 30a^2 + 63a$
5. $2b^2 + 10b + 12$
6. $5x^2 - 15x - 140$

Explanation:

Let's solve problem 22: \( x^2 - 14x + 49 \)

Step 1: Identify the form

The quadratic is in the form \( ax^2 + bx + c \), here \( a = 1 \), \( b = -14 \), \( c = 49 \). We check if it's a perfect square trinomial. A perfect square trinomial has the form \( (x - m)^2 = x^2 - 2mx + m^2 \).

Step 2: Check the middle and constant terms

We need \( -2m = -14 \) (so \( m = 7 \)) and \( m^2 = 49 \) (which is true since \( 7^2 = 49 \)).

Step 3: Factor the trinomial

Using the perfect square trinomial formula, \( x^2 - 14x + 49 = (x - 7)^2 \)

Answer:

\( (x - 7)^2 \)